2000 Passat burning oil smell and smoke under hood

I just purchased (2 days ago) a 2000 Passat GLX V6 with 47300 miles. I've begun to notice a smell of burning oil at times while driving, mostly while stopped or idle. After driving around for a while it will begin to smoke under the hood a little. When I bought it, the dealer informed me that the oil had been changed just recently. I am wondering if he may have spilled any while performing the oil change, causing the smoking. I have noticed some dripping. My dad looked underneath the car and said it looked like there was oil on everything. I put another quart of oil in and noticed that on the bottom of the cap, there was a burnt/charred substance. Is this a possible indication of a damaged engine? Maybe the previous owner let it run out of oil completely? I'm feeling really horrible about this purchase. I'm a student and hope I didn't just waste thousands of dollars buying a car that has a serious problem.
Also, Jiffy Lube said that they believe the problem is that when he changed the oil he may have dripped it everywhere, causing the burning/smoke. They have offered to clean everything up to see if that takes care of the problem. It seems to run very well despite the smoking.