I have a Dell 3007Wfp that has some smudges on it that look like fingerprint smudges, only when I clean the monitor with some electronics cleaning wipes, they don't come off. Any idea what these might be, and how to get them off?
Try using isopropyl alcohol diluted with distilled water, typically found as rubbing alcohol very cheaply in your local grocery store. Since you're specifically going after fingerprints, you'll want to use the 70%/30% version, not the 91% or higher versions.
Anything stronger than isopropyl alcohol will probably make the screen worse, so if that doesn't do it, you're done and stuck with what you got. Do NOT use Windex or any other ammonia-based cleaner on monitor screens because they will permanently stain them yellow.