First of all, you should know that a new ePSXe version has just been released, after 4 years of no updates. Version 1.7.0. Check here for the news:
http://www.ngemu.com/ (Don't worry, this site doesn't distribute ROMs or Bios, just the emulators.)
This version fixes compatibility issues with a lot of games, as well as it improves the mdec playback. So naturally, updating to this version should be the first thing to try out.
The graphics plugins have been updated as well, so it may fix this graphic problem.