I've found that besides this and many other forums (which can be a chore to search through) there are two really good sources of information on diagnosing and fixing these transmissions. Both of them also sell parts to fix them and, while not all of us can afford new parts, the knowledge one can gain through the videos and instructions at these two sites can take the mystery and some of the difficulty out of the job.
The first: https://www.sonnax.com
The Saturn specific tech section is here: Saturn TAAT Tech Resources
I would say that most of the time if someone buys a remanufactured valve body it came from Sonnax.

(The link below seems to be dead as of 12/17/2023)
Another excellent source is: http://www.carsaturnstore.com/
The whole site is Saturn focused but the transmission section is here: Saturn S-Series Transmission Repair Kit - CarSaturn
I've purchased other parts from them and in my case they sent a DVD with full instructions and the same videos they have on youtube.
They also sell remanufactured valve bodies (using Sonnax parts).

If you have access to a machine shop and can do the work yourself you can also buy the Sonnax parts and rebuild the valvebody for just the cost of the parts.

 

Learn-In Procedure
Like many other electronically controlled transmissions the TAAT is adaptive to various transaxle conditions. Ideally the adaptive parameters should be reset using the service stall system (SSS). This of course should only be done after the following have occurred:

• The transaxle has been replaced.
• The line pressure actuator has been replaced.
• New clutch plates have been installed (trans overhaul).
• Valvebody has been replaced.
• The PCM has been replaced.

Of course for most of us, using the SSS to reset those values is not possible but regardless the vehicle will still need to be driven and a learn-in procedure followed for the quickest improvement in drivability. If the official learn-in procedure can't be done for whatever reason the transmission will still eventually learn and adapt to the new conditions. It will just take longer and act strange in the mean time.

1. If there is a shift mode switch - place it in normal mode.
2. Warm up the transmission (oil temp. above 45deg C (113deg F)).
3. Perform 10 sets of upshift (1-2, 2-3, 3-4) at 30% throttle:

 

Valve Body Solenoid Testing

If the solenoid valves go bad you can lose a gear, have poor shifting or not be able to move at all.
Lots of people (including myself) suggest testing the solenoids with a multimeter.

• Normal resistance = 4.5 to 6.0 Ohms. (91-92 actuators are 2.5 to 4.5 Ohms)
• Values should be within 1 Ohm of each other.

If you find resistance lower than the range shown above then the solenoid is shorted. Replace it.
If you find resistance higher than the range shown above then the solenoid is bad. Replace it.

I will find and add an illustration of the connector pinout.

 

Looking at the transmission with the connector off this is the pinout.


TAAT Pinout

The location of the individual solenoids is like so (with cover off).


Solenoid locations

If you find that one or more solenoids needs replaced you will need to remove the top of the valve body and the connector plate.


Connector Plate

The connector plate is somewhat like a printed circuit board and fits over the solenoid pin terminals.
It's a little stiff removing it so you have to be careful not to bend it. Going back on is easier but you have to be sure the solenoid pins are lined up with the holes in the plate.
If there was a shorted solenoid be sure to check for heat damage to the connector plate where it connects to the solenoid and the pins where it connects to the wiring harness.
It can burn out at those locations and require replacement of the connector plate and possibly the harness connector.
The solenoids themselves come out by just pulling with a little twisting motion.

Solenoid actuation shown below (PWM is pulse width modulation - similar to how the fuel injectors are controlled).

 

In addition to checking resistance the solenoids can be tested by actuating them and listening to the sound they make.
They should make a clicking sound and it should sound the same for all five. If one doesn't make a sound or sounds off from the others then that solenoid needs replaced.
There's two methods to do this.

1. For all generations:
Simply apply 12VDC across the solenoid pins. This can be done through the connector or if the cover and connector plate has been removed by connecting directly to the solenoid pins.
The post above shows the terminals and polarity at the connector if you use this method.

2. For 1st and possibly 2nd Gen cars:
The 1st and (and possibly 2nd Gen) have an automatic test routine built into the PCM.
The nice part about this test is that it can be done from the drivers seat and the only tool required is a paper clip.
Jump terminal A to B in the connector as shown in Figure 12.



After the terminals have been jumped, turn the ignition to the "ON" position. Do not start the engine.
Next, move the selector lever into the manual 2 position and listen for a buzzing noise coming from the 2nd actuator.
Use the chart in which illustrates the gear selector position to check the desired actuator.


When the gear selector is moved to the corresponding position, the PCM will pulse width modulate (PWM) the actuator at a set duty cycle for about six seconds.
Listen and compare the noise of the suspected bad actuator to that of the other actuators. They should all be similar.
If the noise coming from the suspected bad actuator is faint or not present, replace the actuator.

 

It can happen that the gear select switch isn't working right.
Pinout:



Check for correct operation by testing each pin to ground:

 

The PCM also uses signals from 3 sensors as part of its data set for controlling the transmission.

Turbine Speed Sensor (TSS)
Vehicle Speed Sensor (VSS)
Both sensors resistance should be between 800 to 1600 ohms.

Transaxle Fluid Temperature Sensor (TFT)
Nearly identical appearance to the ECT and temp./resistance chart is identical.
Maybe they can be swapped?


Sensor locations:



Note, the temperature sensor port doubles as a line pressure test port.
300psi gauge connected there will indicate line pressure.

 

The infamous input shaft nut torque is 111 Ft-lbs.
Any fiddling with the input shaft nut will require the use of red loctite upon reassembly.
The rest of commonly need torque figures in chart below:


TAAT service torque chart
Additional Torque values:
Stator shaft to pump housing bolts.... 30 Nm (22 ft. lbs)
Pump housing to case bolts............. 12 Nm (106 in. lbs)
Park housing to case bolts............... 30 Nm (22 ft. lbs)
Feed pipe to end cover bolts............. 12 Nm (106 in. lbs)
External filter shaft to case............... 31 Nm (23 ft. lbs)
Reverse idler shaft cap bolts............. 20 Nm (15 ft. lbs)
Short housing to case bolts.............. 25 Nm (18 ft. lbs)
Long housing to case bolts............... 28 Nm (21 ft. lbs)
Bell housing to case bolts................ 25 Nm (18 ft. lbs)
Fork to servo stem bolt.................... 10 Nm (89 in. lbs)
Servo piston cover to case bolts....... 20 Nm (15 ft. lbs)
Main (Input) shaft nut...................... 150 Nm (111 ft. lbs)
Counter (Output) shaft nut .............. 150 Nm (111 ft. lbs)
Manual shaft nut (1994 & up)........... 12 Nm (106 in. lbs)
Selector switch to case bolts........... 14 Nm (124 in. lbs)
Manual lever to shaft nut................. 12 Nm (106 in. lbs)
End cover to case bolts.................. 28 Nm (21 ft. lbs)
Upper to lower V.B. bolts................ 11 Nm (97 in. lbs)
Valve body to case bolts................. 11 Nm (97 in. lbs)
Valve body cover bolts.................... 10 Nm (88 in. lbs)
Spring and roller to V.B.................. 12 Nm (106 in. lbs)
Turbine shaft speed sensor............. 26 Nm (19 ft. lbs)
Output shaft speed sensor.............. 26 Nm (19 ft. lbs)
Cooler fittings................................ 29 Nm (21 ft. lbs)
Filler tube to case bolt................... 12 Nm (106 in. lbs)
TFT Sensor.................................... 8 Nm ( 71 in. lbs)

 

Here's some illustrations showing the torque sequence of most covers that get disturbed during repairs.


Valve Body Cover



Valve Body to Case bolts


Solenoid Cover Bolts
(#9 is the retention bolt - install first/remove last)

 

Which bolt is which (valve body)?

Valve body bolt identifier chart

Bolt length guide