OK. So I went and installed the Flash 9 Debug Player, and the installer refused to work unless I ran it from an administrative account.
It wasn't very eloquent, either - the installer failed with a cryptic error message related to not being able to open a folder (you know, one of those obtuse error messages with numeric codes that show that a product wasn't really tested...).
So I ran it under my administration account, and all of a sudden I can't get any Flash content to work - except under my MacBook's administration account (Safari complains about a missing plugin for that MIME type, etc., etc.).
More proof that even traditional Mac developers like Adobe and Macromedia still haven't figured out that Macs have different user privilege levels, I guess.
More importantly, though, anyone know how to fix this completely asinine turn of events?
Update: Reinstalling the plain vanilla plugin and then the debug one worked. I did have to make myself an admin temporarily, though. Go figure.
Update 2: Those of you using TextMate to do ActionScript coding may want to check out the latest bundle update, too. Makes the whole thing a lot easier for simple projects (although I'm still partial to Ben Jackson's approach, which he tells me will be updated soon).