...it is not clear to me that it is well understood why inflation sometimes can be seen in consumer goods and sometimes is manifested in "asset price inflation". Do you have any ideas on this mechanism? I know some people deny there is such a thing as "asset price inflation". Do you have a theoretical basis for your ideas in this area?
I have a very simple answer to this question: Follow the money. Whether an economy generates asset price inflation or consumer price inflation depends on the details of to whom cash flows. In particular, cash flows to the relatively wealthy lead to asset price inflation, while cash-flows to the relatively poor lead to consumer price inflation.
Why? In Keynesian terms, poorer people have a higher marginal propensity to consume. The relatively poor include people who are cash-flow constrained — that is they cannot purchase what they wish to purchase for lack of green, so their marginal dollar gets immediately applied to the shopping list. Also, poorer people may be different, there may be a correlation between poverty and disorganization, lack of impulse control, inability to defer gratification etc. Think of Greg Mankiw's Spenders/Savers model.
Except when the world seems very risky, no one holds cash for very long. Poorer people disproportionately use their cash to purchase goods, while richer people disproportionately "save" by purchasing financial assets. If the supply of both goods and financial assets is not perfectly elastic, then increases in demand will be associated with increases in price. If relative demand for goods and financial assets is a function of the distribution of cash, what price changes occur will be a function of who gets what. 
This tale of two inflations helps to explain how we arrived at the unequal, credit-centric economy we have today. Central bankers are notoriously allergic to "wage pressure" as a harbinger of rising prices. Wages have two distressing properties: First, they are sticky. They represent repeated and persistent cash flows that cannot be downward adjusted en masse except during a serious crisis or dislocation. Second, a substantial fraction of wages goes to lower quintiles of the income distribution, who have a high marginal propensity to consume. Central bankers are not evil scrooges — they have nothing against consumption by poor people. But funding that consumption by wages limits the effectiveness of monetary policy. They'd prefer that the marginal dollar bound for consumption flow from a more malleable source.
During the "Great Moderation" in the US a variety of structural changes helped to increase the potency of monetary policy:
The wage share of GDP decreased significantly over the 1970s and 80s. Compensation did not decrease as much, but much of nonwage compensation is retirement savings that is saved rather than consumed.
Wage inequality increased, such that a growing fraction of wages went to "savers" rather than "spenders", limiting the direct impact of wage growth on consumption.
The growth and "democratization" of consumer credit provided consumers with an alternative source of purchasing power that was sensitive to monetary policy.
Prior to the Great Moderation, central bankers had to provoke recessions in order to control inflation. Broad-based wage growth led to increases in nominal cashflows by "spenders" that could only be tempered by creating unemployment or other conditions under which workers would accept wage concessions. In the post-Reagan world, growth in the sticky component of disposable income shifted to the wealthy, who tend to save rather than spend their raises. The marginal dollar of consumer expenditure switched from wages to borrowed money. The great thing about consumption funded by credit expansion, from a central banker's point of view, is that it is not sticky downward — no one who gets a loan today assumes that she will be able to expand her borrowing by the same amount every year. Credit-based consumption is susceptible to monetary policy with far less impact on employment than wage-based consumption. (One of Ben Bernanke's many claims to fame is his characterization of the credit channel of monetary policy transmission.)
By the middle 2000s, the credit economy was the air we breathed, and conventional wisdom held (and continues to hold) that economic growth and credit expansion are synonymous. We had those peculiar debates about the difference between "consumption equality" and "income equality", and which mattered more, since middle-class consumption had become significantly credit-financed. But from central bankers' perspective, we had stumbled into a good place, one where output growth was channeled into asset price inflation, but provoked consumer price inflation only indirectly and via a channel policymakers could regulate. This benign regime faced two threats, however. First, asset price inflation is unstable — while on any given day, price moves are determined by the flow of funds into assets, over time prices can become so unreasonable relative to the the asset's cash or service flows that arbitrageurs and nervous fundamentalists appear, creating the potential for a collapse. Second, credit expansion is unstable, as chronic borrowers may become unable to service existing debt, let alone borrow more to sustain aggregate demand. Unnervingly, sustaining consumption has required a secular downtrend in the policy interest rate, and eventually you hit that zero-bound. 
The Greenspan/Bernanke doctrine can be summed up by three familiar words, "Yes We Can!" Greenspan famously concluded that we can "mop up" asset price bubbles after they burst, rather than interfering with the dynamic whereby asset price inflation substitutes for consumer price inflation. Bernanke devoted his life to studying the role of credit in monetary policy and the hazards of deflation and credit collapse, and he famously concluded that we have the technology to prevent "it" from happening here. We are watching his experiment play out, in real time and from inside the maze. The outcome is not yet known.
I have my own normative view of "the great moderation", and it is not positive. I do not hope to see a return to the "good old days" of the 1990s and mid-2000s. But that isn't because the moderation dynamic cannot work, in principle. In principle, we can periodically reset the stage with a money-funded jubilee. It'd go like this: When credit expansion reaches its natural limit, let the debtors default, but make creditors whole with new money. "Moral hazard", rather than a problem, is the goal of the operation: Low marginal-propensity-to-consume "savers" are rewarded and encouraged to continue pouring their incomes into domestic financial assets, where any effect on goods price inflation is muted. Over several years, the balance sheets of debtors can be cured via some combination of bankruptcy, loan modifications, austerity, and youth. In the meantime, the Federal government adopts the role of consumer of last resort, in order to sustain nondeflationary levels of aggregate demand and limit unemployment. I think this is our current strategy. We are groping and stumbling towards the status quo ante, and it is not impossible that we will find it within a few years.
So what's the problem? First, in exchange for apparent stability, the central-bank-backstopped "great moderation" has rendered asset prices unreliable as guides to real investment. I think the United States has made terrible aggregate investment decisions over the last 30 years, and will continue to do so as long as a "ride the bubble then hide in banks" strategy pays off. Under the moderation dynamic, resource allocation is managed alternately by compromised capital markets and fiscal stimulators, neither of which make remotely good choices. Second, by relying on credit rather than wages to fund middle-class consumption, the moderation dynamic causes great harm in the form of stress from unwanted financial risk, loss of freedom to pursue nonremunerative activities, and unnecessary catastrophes for isolated families. Finally, maintaining the dynamic requires active use of policy instruments to sustain an inequitable distribution of wealth and income in a manner that I view as unjust. In "good times", central bankers actively suppress the median wage (while applauding increases in the mean wages driven by the upper tail). During the reset phase, policymakers bail out creditors. There is nothing "natural" or "efficient" about these choices.
The great moderation made aggregate GDP and employment numbers look good, and central bankers sincerely believed they were doing a good job. They were wrong. We need to build a system where changes in asset prices reflect the quality of real economic decisions, and where the playing field isn't tilted against the poor and disorganized in the name of promoting price stability.
 "reason" asked about a "theoretical basis". It's important to note that my story betrays an anti-theoretical bias. In the perfect world of financial theory, the supply of financial assets should be infinitely price elastic at one true "fair price", since arbitrageurs can increase supply indefinitely by selling an asset short if it is "overvalued" relative to the value of its future cash flows cash flows. In reality, the capacity of market actors to recognize, let alone to arbitrage away, mispricings is very limited. So cashflows to people more likely to invest than to consume can lead to diverse forms asset price inflation, depending on what sort of assets the cashflow receivers are interested in buying. Further, rather than causing arbitrageurs to short overvalued assets, as theory predicts, high asset prices often provoke entrepreneurs to increase supply by manufacturing similar assets as substitutes, which results in increased real investment in the overvalued sector (while short-selling should in theory help prevent overinvestment).
Also, while "clientele effects" play some role in theories of term structure and the effect of liquidity on asset prices, most theories of asset pricing don't take seriously the idea that patterns of income or access to cash might affect prices. My view is that the asset pricing literature is descriptively wrong, for the most part, although it arguably has normative merit.
 There is a third threat: The increasing stock of assets leaves the system ever more vulnerable to "runs" into commodities or foreign assets. When the stock of assets is small, central banks can contain a run by serving as "market maker of last resort" and managing the cross-price between domestic financial assets and perceived safe havens. When the stock of effectively guaranteed financial assets is large relative to central bank reserves of whatever investors are fleeing to, the central bank may lack the ability to manage price volatility, which might be perceived as a violation of its price stability commitment and lead to further flight by domestic and foreign financial asset holders. This is the currency crisis/dollar collapse/gold bug scenario, and while a large stock of guaranteed assets increases its likelihood, it is by no means a foregone conclusion, especially for large states capable of employing a creative array of fiscal, diplomatic, and legal maneuvers to help manage and control market outcomes.