Obvious things to look for:
- Dirty/burnt transmission fluid
- Slippage when driving (can be hard to detect in an automatic, unless it's very pronounced)
- Very clean transmission fluid (re: are they trying to hide something)
- Check to see if pan/pan gasket looks new (re: are they trying to hide something). If no real pan gasket and has a drain plug, does this area look cleaner than the rest of the engine area?
- While at a stand still and foot firmly on the brake, run the transmission (slowly) between reverse, neutral, and drive several times ... does it seem to shift easily (not by the gear shift, but by feeling what's going on)? Does it seem to be solid when it goes into gear? If it feels like it just sloppily goes into gear (long duration to get into gear), there may be an issue. This is a listen and feel procedure ... what are your senses telling you.
Sometimes the tranny fluid just needs to be changed. Just because the fluid is very clean doesn't mean there's an issue, it's just something to be wary of is all.