How long has it been since the automatic transmission fluid has been changed? Any info from the previous owner on when this was last done?
Dirty fluid can be the cause of hard shifts, and can affect shifting timing as well.
Also check how much fluid you have in there, if you haven't done so already. Low fluid could be the cause as well. Run the car for 10-15 minutes or so travelling a few miles around your neighborhood to warm the fluid. With engine running, and on a level surface, pull the dipstick and check the level.