I also DD an 01.5 S4, as well as being an Audi enthusiast I have a decent amount of experience with most cars in their lineup.
A lot of the common issues have already been mentioned. I am at 110k on original turbos with no symptoms of failure.
Things to watch out for:
Symptoms of turbo failure
Suspension bushings
transmission grinding
timing belt maintenance
wheel bearings
frozen rear calipers
Dead center displays between dials
Bose speaker failures(similar to NSX, although not as spendy to fix)
Buy one as close to OEM as possible, as aftermarket mods like tunes will decrease turbo/clutch life, obviously. Unless you get a well sorted one. Some people prefer to buy ones with upgraded turbos as they are more reliable than stock turbos once the boost is increased.
The cars are very solid, make great DDs, especially in snowy states. The TB, like an NSX, is crucial.
I average about 23 MPG mixed driving.
Some things I dislike about the car:
The interior is small. While there is plenty of room for front occupants, people in the rear will be cramped
The weight distribution is front-heavy. I don't track mine really, so its not really an issue.
The drive by wire system is super laggy. At first I thought my turbos were failing because the spooling took so long, and then I learned that its the throttle lag. Its terriffic for DD duty because it makes everything smooth, but for fun driving it suffers. My APR tune sharpened up the throttle a good deal, though.
The suspension is very soft when OEM. This is a trade off, but I would prefer something a little stiffer with less body roll.
Some things I like:
The interior is very classy and well made. Nice materials for an entry level luxury car. The seats are great and the leather is nice.
The AWD system is the bees knees. Very easy to control and fun in slippery conditions(if thats your thing). It is also a very reliable system as its 100% mechanical.
The car is very smooth and solid, especially as the speeds increase, a common trait for German cars.
The engine is great. Throttle input aside, it pulls strong, hard, and quietly. It is faster than it feels.
Also the looks. IDK what it is but I think its a very handsome car with its subtle styling.