Weird visuals in question: Brick-like effect on 2D, quite disturbing. Happens on a machine with WinXP and a Radeon 9700, for example.
In that case, through the unexpected guidance of Freespace 2_Open I've found a reasonably effective cure! It comes in the shape of registry-tweaking, but Never Fear! I'll walk you through it nice and easy.

Short version (for regedit-literate):
Find FF8's registry-bundle (the one with datadrive e: or whatever, etc) and add the DWORDs D3DTextureDivider and D3DTextureOrigin and set them both to 1. An' that's that.

Long version (for regedit-illiterate):
Fire up regedit (Run->regedit) and navigate to... HKEY_LOCAL_MACHINE\SOFTWARE\Square Soft, Inc\FINAL FANTASY VIII\1.00. Rightclick on an open area in the rightmost frame and select New->DWORD-value/key. Name one D3DTextureDivider, repeat the procedure and name the other one D3DTextureOrigin. Doubleclick each of them and set their values to 1. No strings attached, no chance of screwing your computer up unless you're UNBELIEVABLY clumsy. Really. Well, as long as you follow my instructions to the letter, anyway.

This fix makes the brick-effect on the 2D-backgrounds go away, but the menu still looks a little messed up. Still, it's a perceivable improvement. And FF8 with 6x FSAA... Easy on the eyes. FF8 without FSAA... not so easy on the eyes these days.
If someone knows of a way to make the numbers, you know, resampled to its targeted resolutions, I'm all ears.

Oh, one last thing... Don't "manually" update FF8's Bink-DLL, or the game won't even get past the Eidos-video. :o