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What has changed

The API is gone. The new downloads need 1st to parse the Yahoo Finance page to find a hidden crumb and use it as the key for data retrieval over a 2nd URL.

The adjusted close is sometimes the adjusted, sometimes is the non-adjusted and sometimes is a different value

Lines with literally "null" as the value for the prices have been inserted. Apparently this sometimes only affects the volume

Sometimes changes will appear across a single download of data.

Splits and dividends are for example apparently no longer applied to some of the values

What exactly about the quality of the data has changed (or that changes appear sporadically without explanation, which would be bad) What about the data described has changed (is it adjusted as it was before, or are dividends no longer adjusted for, putting Yahoo! Finance on part with Google Finance)

Having a lot of "sometimes" as seen above is for sure no synonym of quality

What about the data described has changed (is it adjusted as it was before, or are dividends no longer adjusted for, putting Yahoo! Finance on part with Google Finance)

See above again

Whether Yahoo! Finance should be the go-to source for free equities data now, or whether Google Finance/Quandl are now superior

It is obviously no longer usable without a prior analysis from your side. Anything else seems to be a better choice now.

For reference see for example:

Note: Understanding that Yahoo may have not been happy about people downloading (and possibly redistributing) data for (a) f(r)ee, how Yahoo did it shows what Yahoo is up for: a web page that said that engineers were working on the problem. There was obviously no problem and a page indicating that the service was no longer available would have been the right way to go.