I had a problem similar to this and the problem was my mouse (what kind of mouse is on the Mac?) - it was so sensitive that very minor vibrations (like a door closing or a big truck driving by) would cause it to wake up the computer when I had put it to sleep. I simply power down my mouse after putting my Mac to sleep and the problem went away. Turn on the mouse and move it a bit and the system would wake up when I wanted it to, not randomly any longer...
Another possible issue is waking up from network accesses - this is in the "Energy Saver" System Preferences pane (in the Power Adapter tab) - do you have other computers or devices that might be trying to access the iMac while it was asleep?
Good luck...