I've got a '92 STS. I'm trying to think of anything you should look out for...?
My car is pushing 200K, and I haven't really had much trouble after repairing the things that had been neglected when I got it. For instance, the motor-mount going from the side of the block to the front of the powertrain cradle had gone bad (the one that attaches down low on the "front" near the radiator). I also replaced the "dog-bone" mount at the top/front while I was at it- it was a little dry-rotted and I figured the stress from the failed lower mount had probably caused it to loosen some.
Otherwise, I'd say to look for the common things one looks for on older cars- leaks! If you've ever seen/done/paid for any major engine/driveline work on these cars, then you know it ain't no picnic.
I don't think there are a lot of issues on that generation Seville, and if they had some, I think they'd have the majority of them figured out by '91...the 5th and last year of production. Like Doug said, keep an eye out for leaks, just like any other 16 year old car, they'll have their share of those. But other than that, the 4.9L is a rock solid V8, but the early ones are more suseptible to the 4.9L main bearing thump...my '92 has it.
Otherwise, I think they have the computer command ride, which'll mean expensive OEM replacement struts, but I'm sure you know about that, your '99 has a more advanced and expensive version of them.
Other possible issues.....digital dash problems perhaps? I know a lot of the digital dashes used in '80s GM cars had a lot of problems but I can't remember hearing a lot of bad things about the one used in these cars.
I had a '90 Eldorado which is basically the 2 door version of the Seville you're looking into. I really liked that car. The '90 had the 4.5 liter engine which was a great engine. The 4.9 is even better. Actually, the digital dash on those cars were not problematic at all. I had about 100K miles when I sold mine and everything worked fine.
There were really no particular problems with these generation Sevilles and Eldorados. The issues mentioned in previous posts to look out for really pertain to most 16 year old cars, except of course for the Computer Command Ride.
Those cars had OBD, so I would of course check for codes (press the off and warmer buttons on the Climate Control Panel) to see if there are any current or stored history codes set. The only other thing I can think of is the Bose Radio. I had the Bose with the Cassette. I have to rate it as one of the best sounding radios I've had. But unfortunately, the amplifiers are prone to failure after so many years, so if it has the Bose Radio, I would check for that as well.