When I get to the menus, the picture on the menu flashes like crazy and it's hard to use my cursor. After completing a race, text is sometimes strewn across the screen and it's impossible to do anything but exit the game by pressing escape. Other menus like the trophy case can't be exited either. The menus that do work are the options, cars, race select menus, and championships. The game plays just fine and there are no issues there.

My specs (in case it's my problem)
Radeon 6950 2GB
16 GB
i-7 2600k @3.40 GHz
Windows 7 Home Premium 64 bit

I am not using any compatibility settings on the game.

I'm also having some menu issues, similar to yours.
While I don't have the screen flickering you mentioned, my mouse movement is rather slow.

As you mentioned, it is only in the menus (some are worse than others) and gameplay wise everything is fine.

Having said all of that, it's not really a big issue as I'm only in the menu long enough to set some controls and them I'm away.

Specs:
Windows 7 Home Premium 32-bit
Intel(R) G41 Express Chipset
Intel Celeron E3400 (2.60GHz)
4GB RAM

Same issue here - resolved by opening ps_clo.exe and ticking "-forced3d", hitting OK, then opening the game.

My menus are woking ok, but has a slight delay. Sometimes not responding.

Also, the intro videos plays sound but no display. Skips normally to main menu.

I found a half-working fix, right next to the Powerslide play button on GOG Galaxy click on 'more' then click on 'other', then click on config. You will see a small menu, under graphics select '-forced3d'

This will force the Glide API to work on Direct3D. Unfortunately this causes some of the textures to be pixelated and runs slower. The intro videos is now working and the menus is functioning normally.