> Housing prices can go up by 20% a year for 5 years and there's still no "inflation".
No one will have any idea whether inflation is happening or not by looking at a single market. That's why CPI doesn't do that. Housing prices could increase 2.5x in five years and not be an indicator of inflation, although that seems unlikely. But without examining a large sample of other markets, it's nearly a pure guess.
> Here's the problem - we use the Consumer Price Index to measure inflation, of which "housing" is only 33% - much of which is actually rent, which is quite a bit more inelastic than home prices.
Demand for housing across the board is inelastic (notwithstanding vacation homes or other "second" homes, in which demand is elastic and also a very niche market). Demand for credit is elastic, and so increases in the price of credit, i.e. the interest rate, will cause potential home-buyers to substitute into being renters.
> If someone buys an 8 unit condo building in 1980 and rents out each unit for a 20% profit, 20 years later they're still making a 20% annualized profit and maybe rent hasn't increased.
There's not enough information here to understand this scenario. It's not at all obvious that the landlord in 2000 is making an annualized profit of 20% unless he's the king of slum lords. Not only will maintenance and other recurring costs increase as inflation increases, the opportunity cost of the landlord using the land to house renters as compared to other productive uses of the land will also increase in nominal terms (and probably also in real terms unless the local economy is dysfunctional). Those costs - both the accounting and opportunity costs - will be passed onto the renters.
> Asset inflation is inflation.
Typically in economics, an increase in the "general price level" is inflation. In micro terms, inflation means the aggregated prices across all markets have increased relative to money, i.e. the increase is not accounted for by income or substitution effects. This doesn't mean all markets will be affected with equal price increases or anything. We'd still expect markets with inelastic demand to have higher price increases and markets with very elastic demand to have small price increases (though competitive markets will probably also have some shenanigans with quantity restriction, which aren't captured by the supply-demand model). We'd also expect some noise from various markets due to peculiar circumstances unique to each market. E.g. a potato blight creates a supply shock that causes a drastic increase in the price of potatoes, and which could have ripples in decreases in prices of complements and increases in prices of substitutes which is non-inflationary.
> That "real" inflation, also known as the consumer price index, hasn't been going up is a factor of both automation/economies of scale and an extremely bifurcated economy in which low end workers are making pennies, toilet paper is cheap, but a house in an area with a working economy costs triple what it did 10 years ago.
CPI is just a measure of inflation, i.e. the general increase in prices across aggregated markets, that uses sampling. (Also, the word "real" is overloaded in economics, and means changes that take into account inflation or, alternatively, ignore the use of money.) Inflation is quite tricky to measure, and so CPI must make loads of assumptions about substitutes, complements, and income effects (e.g. technological progress, economies of scale, productivity, etc.).
Also, for point of comparison, the minimum wage in CA has doubled since 2001, but the price level has not. It's a similar story in New York, Massachusetts, Illinois and Washington (and presumably other blue states). Red states like Texas or Florida have not had a significant de jure increase beyond the federal level in that time, though if I were to guess, the market minimum wage is simply above the legal minimum wage in those areas. It seems likely that low-end workers are making more, middle-income workers have stagnated and then upper-income workers have seen their income skyrocket.