Hi Will, first of all, 120k is not huge mileage for these engines if they have been maintained correctly. Take a look at the stickies, there is a good guide in there. Key things to look out for:
Servicing - the S3 can have the Audi "Long Life" service intervals (20k miles/2yrs I believe, with specific "Long Life" oil), but it's better to see regular 12k/1yr stamps in the book. Don't necessarily think that Dealerships are better - in my experience (and others on here) you actually get better service from a reputable independent VAG specialist. Make sure the Haldex oil has been changed every 20k and filter every 40k. Check cambelt done at around 65k or 5 yrs.
Haldex - make sure the car is running 4WD. It's "on demand" 4WD on these cars, not permanent. Pulling the handbrake up one notch will dis-able the Haldex, leaving FWD only. You can really notice the difference, even in the dry under medium-hard acceleration, so try it.
Rear diff - make sure it doesn't whine and that on full lock the rear wheels do not bind at all. Some people have reported problems with this.
Door sensors -can play up so the car thinks the door's open when it's closed. If so this will cause the interior light to stay on when shut, and the alarm will not activate. Check it. Will need replacing if faulty.
Alarm - batteries in the alarm system eventually die. When turning the car off you may hear 3 beeps coming from the boot area if they're dead. Easy fix though.
Suspension - check for clonking from front (top mounts) and if you can, get under the rear and check the rear springs are not cracked at the bottom of the coils (common failure around this mileage).
Windows - check they go all the way down & up again. The runners can fail over time. Easy enough to fix though.
Door blades - make sure they're securely attached & flush with the doors. Over time the internal components start to separate. Can be fixed though.
Obviously give the car a good inspection & test drive before parting with your cash!
Generally, these are great cars, very reliable with good build quality and performance. The points above are just a list of common things that I can think of. Best of all, this forum is fantastic with lots of free advice and expertise on hand. I've had my '03 BAM for 3 years now and I have to say it's been fantastic. I've used this forum countless times to solve problems, make some modifications and discuss ideas.
Do you have details of the ad? Might be able to offer more advice if you can post the ad and some pics of the car.