What effect does a dirty reference have on the game? Will it increase CTD or slow framerate? What is the best program to use to clean a mod and how do I do it?

dirt reference is either two things:
1 - a saved reference that's exactly the same as the master files. this can cause compatibility issues if an earlier loaded mod changed that reference, and the dirty mod basically undoes this.
2 - data from the construction set when making mods without tribunal and bloodmoon dependancies. this saves some erroneous data considered dirt.

#2 are incorrect game settings (GMSTs) that can cause issues like werewolf forms not working properly or graphical issues like "s" in front of skill names. The UESP has a http://uesp.net/wiki/Tes3Mod:GMST_Contamination on it and how to avoid it.