When do you know that you have a problem with your transmission system?
One indication is delayed engagement. This happens when there is long delay between the time when you shift the shifter into D or R and the transmission in P start the engine, and wait until the engine has reached down to normal level.

Another indication is the slipping. When the transmission problem is excessively worn, it may slip. Meaning the speed remains though you press the accelerator. It is advised that you try driving at all speeds one by one. Every speed should shift smooth and easily without producing noises or jerks.