1992 Nissan Maxima Automatic Transmission Problems

Transmission problem
1992 Nissan Maxima Front Wheel Drive Automatic 188000 miles

I own a 1992 Nissan Maxima which works well when it is up and running. However, within recent times, the AT transmission has not been performing well. The signs of this are: (1) from a cold start, the shift from 2nd gear to 3rd is not done automatically and sometimes when it does change on its own, it works for a little while and then it sounds as if it is slipping. To counteract this I will usually build up my speed in 2nd gear and then manually shift it into drive to engage the 3rd gear and then the automatic shifting will work almost perfectly for the balance of the day. (2) most recently and again from a cold start, the car will not immediately move off as the first gear does not engage until after about 2-3 minutes of idling. I recently changed the transmission fluid (the last such change was about one year agao) although the old fluid was not smelling burnt and there are no visible signs of a leak. Can you guys identify the problem and a possible solution?