So, I'm experiencing square glows, explosions and the likes.

Any advice?

Check the C&C3 forum, we're not really the best place to ask about that.

Okay, well, C&C3 apparently doesn't like CCC 10.6 so I checked for updates and boom. There was 10.7 already out.

Downloading.

EDIT: Didn't help.

So, there are black boxes around all the various glows and such, as if it the black were supposed to be transparent but isn't? That usually comes from an insufficient graphics card in my experience.

No, not black. Like this: http://forums.commandandconquer.com/jforum/posts/list/43303.page

Your troopers learned Trine, from the looks of it. That's pretty cool, from the looks of it.

Do you happen to have an ATI card?
I remember having a similar issue when running Mass Effect on my old 1950XTX.
The glows were all pixelated and sometimes not transparent.

Yep, ATI Radeon HD 4870

Well... That clears the 'Why?' part of the issue.
I dunno how to fix it though. :\

Tried Vsync? It always help me when I get graphical artifacts, I was getting them like mad on Company of Heroes, in the form of massive green squares on the floor.