Anton, I'll bite: this would be just as useful as having a place on the internet which would list well known errors in the papers and follow-ups. Here is a recent example from personal experience: when I was selecting a textbook for an abstract algebra course, I spent several days tracking changes to different editions of Gallian. Of course, a book's reputation is often based on an earlier edition. Note that not even all textbooks (let alone editions) are reviewed by MR, and when they are, this kind of information isn't always emphasized.

Sure, it would be nice to have an agreed upon place on the internet for recording and correcting errors in papers or books, but that's not what the question is proposing. If I'm reading a paper or a book, it's reasonable for me to ask, "where can I find a list of errata?" However, I just can't imagine anybody ever saying to themselves, "I'd really like to find a list of books whose previous editions were better." You would only be interested in that information if you were already inquiring about a particular book, in which case the right thing to do is to go read the amazon reviews. I simply cannot imagine how producing a list of such books in one place would be a valuable resource. Why would anybody be interested only in books that have gotten worse with a new edition, rather than, say, good books on a given subject? (Sorry, I know this comes off as a bit indignant, but I really am baffled.)

When choosing some mathematics book to study, is it always the case that one should look for the current edition of the book. Are there any examples when the older edition of some book is clearly better than the latest version?

Additional motivation:

How do I vote to reopen this question? I think it is very useful to know (and not at all subjective) when a new edition omits sections of the old, changes notation, introduces new errors, etc. – John Stillwell 9 hours ago

For the record, I agree with John.

Anton, I'll bite: this would be just as useful as having a place on the internet which would list well known errors in the papers and follow-ups. Here is a recent example from personal experience: when I was selecting a textbook for an abstract algebra course, I spent several days tracking changes to different editions of Gallian. Of course, a book's reputation is often based on an earlier edition. Note that not even all textbooks (let alone editions) are reviewed by MR, and when they are, this kind of information isn't always emphasized.