The IIIF is easy to work on. Assuming that the shutter tensions are good and the problem is a dirty slowspeed escapement. Remove the 4 chrome screws where the top comes down to the sides, remove the 2 black screws one on each side of the lens flange, remove the bottom chrome cover (this is the cover you remove in order to load the camera with film). Push up on the bottom of the camera innards as you hold the outer shell and the innards will come out. Note that the pressure plate is now free and there are 2 springs underneath it, don't loose them. Remove the 4 screws in the lens flange, watch out for shims and note there locations. Remove the 4 screws under the lens flange (these hold the baffles in place). Remove 2 screw on the left, one by the slow speed dial and the other just a little below the slow speed dial, remove 2 screws on the right. Now the plate the slowspeed dial is mounted on can be lifted and slid down, make sure the rangefinder follower is pushed in so the plate can clear. Now you can see the slow speed escapement at the bottom, flush clean it with lighter fluid and dry with compressed air. When installing the plate with the slow speed dial, set the dial to "T", note the lever that rides on a side lobe cam on the slow speed (backside of plate), makesure the lever is rubbing against the cam, slide plate on (remember to push rangefinder follower in) and there is a little window at the bottom left of the plate where you can see the bottom end of the lever mentioned above, well the end of the lever needs to go towards the right so that it catches into the escapement control bracket (I use a small needle to push the lever to the right), when it is in the correct position the plate will drop down into correct position. Reinstall screws into plate and baffles. Now you can cock the shutter and test the slow speed (yes you are doing it out of the camera body, this is safe to do). If everything is workign correctly then finish reassembly.
If the slow speeds are way off, then you might have the dial out of adjustment or the shutter curtain tension is off. The worm drive screw closest to the front of the camera (under the bottom plate at the bottom of the camera, held in place by 1 large head screw and 2 tiny screws).is the second curtain adjustment. The tension is set so that the slow speed at 1 second is correct. Now check the high speed setting by looking at the film gate against a bright light and firing the shutter. If you don't see a full frame, increase the tension on the worm gear at the back of the camera. Adjust until you have a full frame at high speeds, it helps to use a business card to block one side of the film gate and fire the shutter to see light and then perform the same on the other side. Sometimes the highest speeds are not attainable until the camera has been completely cleaned.
If the dial is out of adjustment, remove the set screw in the slow speed knob and unscrew the knob, loosen the screw underneath and you will see a collar with screwdriver notches in it, counter clockwise pulls the slow speed cam out which decreases the time setting. Adjust the knob so that "T" disengages when the dial is set to "1".