I was test driving a 98 s70 yesterday. It's an automatic. When I put it in sport shift mode and floor it, it pulls hard to ~65 mph, then it wont shift into 3rd. If I let off the gas when it gets up to ~65, then it shifts into 3rd.
Any ideas what the problem could be?

 

well... the transmissions on these car sometimes get a bit of gunk in them that will cause abnormal/ harsh shifting. A manual (don't pay a shop to do it using the rip- off machine) flush usually does the trick. I'd get it checked out for sure, though, before buying the car. Sport shift mode DOES hold out the shifts longer, and RPMS will get pretty close to redline if you have it floored in that mode. If it shifts okay otherwise, it may only need a flush. There's instructions on how to do it around here, and all you need is a piece of vinyl tubing, a couple clamps, a drain pan, and lots of fluid. Again, if this is a car you're looking at buying, have a trusted mechanic- preferably a Volvo specialist or a Euro specialist- look it over first, and at minimum, use this as a bargaining chip, though if the trans itself is on its way out, that's a "no buy" unless the owner is willing to pay for the work.