Seems to happen only when a new turn begins, and then only sometimes. It's actually a very frustrating problem because it happens way too often and I have to minimize the game screen and bring it back up again to fix it.

And sometimes I have to do this before I can make my move because trying to rope through Worms: Psychedelia is akin to playing paintball in heavy fog.

Btw, I'm running it on XP, and I'm pretty sure I've played Armageddon on this computer without any problems before.

This is a common problem that crops up on these forums alot. It is usually caused by: Wrong format custom graves and flags etc or having a program with "always on top" running whilst playing the game.

Winamp and MSN can be main culprits. I get away with Winamp by simply minimizing it and turning off the "always on top " option.

Also make sure you have updated the game witht the latest patch beta 3.***

How would I go about identifying problematic programs and fixing them?

It's not the custom graves/flags thing because I don't have any of those.

How would I go about identifying problematic programs and fixing them?You would check what programs are set to "always on top", including programs like Stardock's ObjectDock, Winamp, various IM clients, etc. Personally, I had a problem with a plugin for bbLean (Blackbox Lean, an Explorer replacement) called bbIconBox when I had it set to "auto hide". There are many programs that have features like this. You don't have to close the programs completely; just disable the erroneous feature(s) (Usually "always on top". The only other one I've found is "auto hide".).

You would check what programs are set to "always on top"Uh huh, and how would I do that?

For further clarification, there are no programs running in windows (as in minimizable windows, not the OS) except for my internet explorer (Juno) when I play Armageddon and the problem still arises frequently.

there are no programs running in windows (as in minimizable windows, not the OS)
Then have a look at the programs minimized to your system tray, i.e. the symbols next to your clock on the bottom right.