my 2002 camry automatic tends to jerk and stutter between 2nd and 3 rd gears only when it has been driven for more than 30 minutes.

That is very difficult to help you from here, but just a word of advice: If somebody tries to talk you in to a transmission flush do NOT allow it. There is a filter screen and a magnet, to collect metal 'dust' on the bottom of the pan. A flush picks up all that and small debris and circulates it through your transmission, doing far more harm than benefit. But begin with checking the fluid, if it is low, only add 1/2 quart Check with engine running, at normal operating temperature, in Park. If the fluid is not a nice pink/red, and/or has a distinct burnt odor, do a drain and fill. That is not too awfully expensive, and worth a try before heading to the transmission shop. Don't you just love Aamco commercials? "Half the people that come to Aamco don't need a new transmission!" Why don't they say "Half the people that come here we stick it to them for a transmission whether they need it or not"

A good high-end scanner will pick up on transmission faults. probably not the one they use to do a 'free' scan, because AutoZone does not sell internal transmission parts ..not to mention you have a good chance the guy scanning it has had a 5-minute training course. Now SOME of them do know what they are doing though