This list is probably not exhaustive. I'll add to it as I stumble upon things. To start with :

System specification as dumped by PC Probe

Dxdiag output 

Yes. Had no problems. Game launches every time with proper screen resolution and music playing.

No. Didn't have a CTD yet.

Yes. One freeze at ending turn. One freeze at Alt-Tabing back into the game from desktop (using fulscreen mode)

No speed issues as such. Going into and out of kingdom management menu is sluggish when compared with going into and out of game options.

It did at first run with default settings (blank world bug). After first exit writing adjusted config no further problems (except loading saved games, see below).

Yes. Saving game doesn't store save time-stamp. Loading game is all messed up and affects all further game interaction (there's a number of threads about this). Other bugs encountered (and reported on the forums already) : eternal ogre den, enemy units rendered on wrong tiles, enemy units visible from under FOW, wrong mine placement, wrong mine size, enemies starting next to each other, river mouths drawn in the ocean, unresarchable techs (veteran, expert, elite units), eternal leftwards scrolling (seems to happen only at max zoom values), no scrolling at screen borders, auto-explore avoiding items and lairs, buildings being completed in parallel not successive order, erratic road building.

Bugs encountered I didn't see mentioned (or probably just missed) :

-Royal palace can be build in more than one copy. Given description and the fact that it can be built only once I'd expect it to be limited to one instance (and maybe spanning over a whole tile instead just a quarter of it) At the moment you can order any number of parallel builds in single city.

-Sometimes conquered cities are not rendered correctly in building view. Example

-Some more river madness. Adding since it's the first time I've seen river mouth inside a landmass (not adjacent to ocean). Screen