Holy ***, i'm experiencing a similar problem now, too.
This seems to be down to some code problems
However, it doesnt happen with any backgrounds, but explosion / beam images. Sometimes, when an explosion ANI starts, or a beam graphic (beam as well as beamglow) are started they are white rectangles - but switch back to the intended graphic about 1 second later.
There seems to be something wrong with the way textures are loaded mid-mission.
Also, I had another worrying bug. You might remember the vanishing textures thingy.... Well, I played some missions in a row again - and suddenly it crashed me out during mission loading saying 'Error parsing briefing_icons.tbl - Missing Briefing icon', and crashed my whole system (so I had to do a hardware reset).
After that, I restarted the game, and it loaded up fine.
So - there seems to be something screwing up so FS2 doesn't find the files anymore (this could also lead to the invisible texture thingy), and there also seems to be something wrong with loading textures in a mission (see white squares problem).