Transmission fluid was replaced a couple months ago, and oil was changed more recently (both were dirty). When I'm just accelerating to say 30 MPH, it doesn't shift until past ~3500 RPMs, then again past ~3100. It slightly lurches when it shifts, quite noticeable. Definitely working too hard. Drives fine on the highway, though! Just bad with city driving.

Oh, it has >200k miles on it by the way. Engine was apparently redone by a previous owner (and works fine), but I don't believe the transmission was. What should I check? What might be the problem?