There are two kinds of transmissions.
1) Mechanical - no electronics and use a valve body to determine shifting pressure..does not throw a code due to it not being electronic to diagnose it youll need to open it up.
2) Electronic - uses eletronics to control and shift the tranny, these can be modded to change line pressures and will throw codes when broken.
Mechanicals are more reliable due to less working parts to go wrong. Also in a race application, drag perf., mechanical trannies can be built to high extremes much like on top fuel dragsters and ect. These trannys are solid and are usually built for racing. Electronic trannies are in newer cars and use a control box/ecu to control shifting point, shifting pressure and so on. These arent ideal to race with because you have to use a shift kit to alter line pressure which isnt that consistant and could ruin the car.
As for your car, there could be several things wrong.
Your stall convertor is going out, and its not keeping your tranny idled right.
You have a crack in your bellhousing and its leaking oil, but i doubt that..unless you revved it up and then dropped it into drive. This would also lead to bad planetary gears which would have been grinded down from bump shifting it.