With Firefox 3.6 from the official repository, and the flash-player-plugin from Slacky.eu installed here. It's worked fine - up until now, where websites either claim it's not installed, or show a blank box instead.
NoScript is installed on my Firefox, but given that on fully trusted pages (of which there are very few) it still happens, and nothing else blocks Flash besides AdBlock and Firefox's own settings (both checked too) I suspect the plugin.
I also tried downloading direct from Adobe, and plonking the libflashplayer.so in /usr/lib/mozilla/plugins and making a backup of the original one (The one provided from Slacky's package) but to no avail.

So it seems to be the plugin, but for inexplicable reasons.
Would anyone happen to be able to explicate this inexplicability?

Try or similar based on name of plugin filename and see if there is some missing dependency.
AFAIK current Adobe's flashplayer library needs dependency provided by seamonkey-solibs package.

Based off the output of that, it looks like everything is there. seamonkey-solibs wasn't installed, but installing it doesn't seem to have changed anything, except now almost all flash shows up as a grey box, instead of some sites claiming it isn't there.

What does aboutlugins (about plugins... since LQ turns a colon and a p into a smiley) show in Firefox?

The relevent part shows the following:

Shockwave Flash

File: libflashplayer.so
Version:
Shockwave Flash 10.0 r42

MIME Type Description Suffixes Enabled
application/x-shockwave-flash Shockwave Flash swf Yes
application/futuresplash FutureSplash Player spl Yes

I'd make absolutely sure if javascript is enabled, ie I'd temporarily disable Noscript. For loading of flash video, scripts may depend on data from other domains then you are currently visiting.

I tried a page with a few flash applets on, fully disabling Noscript, and I'm afraid it still happens.

Check permissions for owner and group on 'libflashplayer.so'. I had the same problem with libflashplayer-10.0.45.2.linux-x86_64...

I think what it has is right - owner root - read and write, group root - read only, others - read, allow executing as a program checked. That's what Nautilus reports.

Mine came out as user 'brz' and group 'vboxusers'. Firefox don't even showed it installed.

It shows up for me, perfectly fine, oddly. Firefox can see it, Seamonkey too, though it's one might be stored elsewhere.
I've thought of trying GNash, except AFAIK it's not been worked on for some time, and is missing a fair bit of support. Could be wrong though.

make sure you only have ONE instance of it trying to open

Usually only ever do have it appearing once. I don't use pages with Flash all that often.