Not really sure of the extent of your texture problems, but mass Effect did have a few issues.
1 example was Garrus looking very low quality.
There was also some texture popping issues in the game, but nothing to bad.
I believe this was fixed with the latest patch. So make sure you have patched to the latest.
And as already mentioned, turning film grain off does help.
(Bit off topic but, I always do this on any game that offers it though, simply because I can not stand the look of FilmGrain)