I see this quite often... in Adobe Song.

I recall that the generic explanation for why this happens (but only in a few cases for a few people) was "poor hinting". And I also recall, with less confidence, that the fix suggested was "go grab your old Baskerville off of your old Mac."

Well, I don't have any solutions for you, but I can suggest an experiment to try.

I don't know how well it will work with your workflow, so be cautious. I have a few fonts like this - mostly for languages like Khmer or Burmese - that work fine everywhere but in ID. So I have slightly-edited versions of some of these fonts, that work okay in ID but cause Font Book (or Word, or whatever) to freak out. So I install the font twice.

Now, this is is generally bad InDesign practice - having the same font installed in multiple locations can cause problems, hence my advice that you use caution. I've not tested this plan at all, so you should before you rely on it.

Whatever changes were made between Baskervilles are obviously required for Mountain Lion. I am 99% sure that you do not have a corrupt version of Baskerville in Mountain Lion. Like I said, Apple make these little changes all the time.

Use the InDesign fonts folder - if you dig into the InDesign folder in Applications, you'll see a "Fonts" folder. InDesign can use fonts in this folder, but no other application can use these fonts. So keep the version of Baskerville that came with Mountain Lion installed in /Library/Fonts, or wherever Font Book keeps it (???), and drop the old Snow Leopard version of the font into /Applications/something/InDesign/Fonts.

This might work, but I've not tested it at all (I have a MBP at home, but my workplace is pretty much a Microsoft shop, the newest Mac we have is a mirror-door G4). So test this carefully before relying on it, if my two-fonts-installed dodge works at all. I've crossed my fingers for you...

Should I log a bug somewhere with Adobe?

That's the community-minded thing to do.

I suggest you insert a link to this thread, because if I were in charge of generic bug-sorting I'd say "Oh, that is a problem with Baskerville, not with ID" and round-file the bug report. But I am going to resubmit my bug, too, which is a problem with one of the Chinese fonts that is packaged with InDesign (!!!), and so maybe if we both submit the bug at the same time it will stand a better chance of being looked at by someone who can do something about it.

Thus I assume that if a font exists in both places, ID uses the one in the application folder over the one in the system.

You know, the Accepted Wisdom on these forums is that what we are doing (installiing two fonts with the same name in different places) is a Bad Idea. Your assumption is a little faulty; it will usually use the one in the /InDesign/Fonts folder instead of the OS Fonts folder. The rest of the time, it'll do something funky, or drop the italics, or crash, or something like that. Be especially vigilant when packaging or exporting PDFs or using Find Font or anything else along those lines. Those are the times that I have seen problems crop up when using this little duct-tape hack.

Whoops! Feature request/bug report is here. If you have a support contract with Adobe, use that instead.

Oh wait, for that you have to mark an answer of your choice as "correct". You can also mark several as "helpful".