In Red Faction 1 this happens with all mirrors in the bathrooms and also the same effect can be seen on all security monitors. Another problem related to this is to do with the screen on the rocket launcher; it always is composed of vertical yellow lines similar to this image.

Does anyone know of a way to fix this?

Here is the rocket launcher glitch. Note that the rocket launcher always looks like this, except on rare occasions when it's screen is completely transparent making it look like there is no screen.

These glitches are present in both the standard GOG release of Red Faction and the unofficial patch, Pure Faction.
I'm running Red Faction on Windows 8.1 and have one of those weird Intel HD graphics cards, if you can call them that.