
My experience years ago going to a film SLR from a compact 35mm camera taught me one thing: more control means more ways to mess up the image!
While SLRs offer you far more creative control, focussing is far more critical, they are much less convenient to carry around. (to the extent that i have a digital compact as well as a DSLR to keep in my bag)
DSLRs also suffer from sensor dust. Olympus has a neat solution to this problem, but for everyone else, there's this: http://www.pbase.com/copperhill/ccd_cleaning
If you don't fancy that, i suggest you steer clear of DSLRs.
One of the biggest differences used to be that DSLRs did what you wanted when you wanted, and compacts took all day to do anything (including actually opening the shutter!) however, today, there are compacts around that are fast enough not to cause a problem, but check that the model you buy doesn't suffer from "shutter lag" by reading lots of reviews, and find out how long it takes from taking one photo until you can shoot the next.