I bought an '88 745T last spring that had similar behavior. The tranny you have is the AW71 which is a 3 speed automatic tranny with an overdrive. Furthermore, you may also have a lockup torque converter feature for even greater fuel economy. This lockup feature is not found on turbo cars, so I don't have it. This posting is a long, but hopefully helpful.

As I said, my car behaved in a similar manner when I bought it. When put into gear with the brake on, it would squat a little and vibrate. I found the engine mounts were toast. Since your car has so many miles, I would consider replacing the engine mounts if they have not been replaced recently. Chances are the engine has settled onto the cross member to some degree. This will transmit vibration to the body of the car, and potentially damage the oil pan. Also, it can cause funny movements of the car since the torque of the engine is no longer isolated by the mounts. These are hydraulic mounts that are rather expensive. Check with places like IPD or a good foreign auto parts store for these. IPD has them for $89 each, my local foreign parts store has them for $75 each, my local dealer once gave me a price quote of $160 each. Guess where I did not go for these parts. Replacing the mounts is a little involved, but not too bad if you have the usual tools and a bottle jack or hoist.

Also clean the throttle body and idle control valve. These get gunked up over time and should be cleaned every couple of years. Chances are yours has not been cleaned in awhile. The job is faily easy and only requires some hand tools and a can of spray carb/FI cleaner. Make sure the idle control valve is free and working smoothly. If it sticks and can not be freed, then replacement is necessary. A bit expensive, but shop around. Volvo sold me one for $180, but I hear a good foreign auto parts store can get a Bosch replacement in the $130 range. This will smooth out the idle a lot. It will also smooth out the transition between an unloaded engine in neutral, and a loaded engine when in gear.

Now for the not so smooth shifting between gears. The shift is controlled by hydraulic pressure through a series of valves inside the transmission. The smoothness of the shifts is somewhat controlled by the size of some small rubber balls in the valve body. Some of these balls wear with age and the change in size will effect the smoothness of the shift. This repair is involved since the valve body needs to be removed and is not a job for the faint of heart. Another thing that can cause harsh shifting are sticky valves in the transmission. This is due to old oil in the transmission. It is not uncommon for people to never change their tranny oil. So after several years, the oils breaks down and forms varnish in the valve body. This effects the smooth movement of the valves, hence the smoothness of the shifts. The usual fix here is to replace the oil and flush the whole tranny. Dropping the pan is not enough since most of the oil is contained in the torque converter. However, there is a warning here. If your tranny oil has never been changed or is several years old, there is the danger that new oil will dislodge some of the varnish and really screw up the valves. In which case, the only fix may be a total tranny rebuild. My father owned a tranny shop for awhile and he learned this the hard way.

As for the delayed shift into 3rd gear, again gunk in the valve body can cause this. Most likely however, the shifting cable that attaches to the throttle linkage is probably sticking. If the cable does not retract properly when you let off the gas while accelerating, the shift to third will be delayed and the engine will rev. to higher than necessary rpm. You can try to oil the cable at the throttle linkage. If this does not work, then replacement of the cable is in order.

As for my car, the harsh shifting has improved dramtically on its own. I have not done anything to the tranny since I bought the car. If could be the difference in driving habits that allowed the tranny to somewhat cure itself. I drive a lot of mixed city and high speed country. The previous owner did nothing but stop and go New York City driving which is hard on a tranny. The delayed shift into 3rd gear has also improved a little with time, probably for the same reason as the harsh shifting has improved. But it is still a bit of a problem. I have found my shift cable is sticking somewhat and it will need to be replaced since oiling has not helped.

As for changing the oil, I am going to try something a little different than the usual flush. Since I fear a flush can initiate a tranny failure, I plan to change the oil slowly. The gunk did not build up all at once, so maybe it should not be removed all at once with fresh oil. I plan on dropping the pan to replace the shifting cable and oil filter. I will then put the pan back on and refill the oil. This should replace about 1/3 of the oil. I will then drive the car for a few weeks. Then I will drain the pan again, and refill. This will remove some more of the old oil and gunk. Doing this every few weeks for a couple months will eventually remove essentially all the old oil and hopefully most of the gunk in a slow fashion. If I still have a tranny failure, then I will have to rebuild the tranny. If time and logistics allow, I think I may do it myself. I have the Volvo shop manuals on the AW71, and the rebuild job does not look to bad if one takes their time and does not mix up any of the parts. The manuals are TP 30871/1 (fault tracing, repairs, and maintenance) and TP 30941/1 (rebuilding). Both are available at 1-800-25-VOLVO. Price is something like $23.50 each. A rebuild kit for this transmission is maybe $150, a good tranny shop will want between $1000 and $1200 to do the work.

Like I said, this posting is long. But I hope it is helpful.