I myself was under the impression that a Ditto could breed with EVERY group except for the No Eggs group. However, I have been trying to breed a Ditto with every single pokemon that I own, yet they are incompatible. Have I been wrong, or is there seriously something wrong with my game? Because I'm focusing on trying to breed all of the pokemon I can so I can finally get all of the baby pokemon. It is REALLY annoying.

What exactly do you mean, they're "incompatible"? What does the daycare man say when you talk to him about your two pokemon?
Also, this might be helpful, if you haven't looked at it already.

He says that they prefer to play with other pokemon than each other. I've been going at this for about 5 hours every day, yet they aren't producing anything. Should I just catch another Ditto or what?

Try catching another Ditto. Ditto CAN breed with any pokemon that can have eggs, but the "They prefer to play with other pokemon" means there's something up with those specific pokemon that gives them a 0% chance of having an egg together. Details on the old man's phrases and their relative chances of egg hatching are in the link I gave you. I don't really understand what causes specific pokemon to have those chances with each other, but that's what they mean.