First go to your Documents\BioWare\Mass Effect\Config\BioInput.ini and in the file you opened, search for [Engine.Console], and add the line ConsoleKey=Tilde just under it.
If you don't have an english keyboard, you may have to type ConsoleKey=Tab

When in game, activate the console by pressing the tilde key (or tab key). The game console will appear. In it, type

viewmode unlit

And play through the parts with the bug. To reset the lighting type:

viewmode lit

You can also save and reload to reset.