Another common issue is the tape counter. The 2 tiny belts that operate it often become hard and the counter itself can get noisy (screechy to be precise).
Personally, I don't use the counter very much so I've simply cut the old belts off. Replacing the belts (if you can find them) is not a trivial matter and requires the removal of the capstan motor and reversing roller.
I actually fiddled a little and managed to change the belt that goes onto the capstan without removing the capstan assembly at all, all you need is patience and looping the belt over the capstan, a thin piece of metal with a tiny l-shaped hook made from a straitened paper clip ought to do it. I used a piece of metal I had lying around anyway. A similar piece with plastic on it, usually used for keeping cables organised should work too.
In my opinion the less parts you disturb during any process of restoring the better, so I did not want to unmount any prt I did not absolutely have to.
Other than that, just check to be sure the brakes, pinch roller pressure and tape tensions are all at spec (I usually adjust the brake tension lower than the factory spec since I play lots of really old acetate tapes which are very fragile) and take care of issues as if they come up.
If you plan to use the machines for use with important tapes, I suggest taking it to a professional shop at least once, to have everything checked over, adjusted and cleaned. That will give you a baseline for the machines performance.
The investment of a couple of hundred bucks will go a long way to protect high dollar tapes or ones that contain your creative output.
A good mod for the tape path, which depending on your exact needs with fragile tape may be a good investment, is to make the fixed tape guides movable, by installing smaller rollers in their place. That includes the two arms pulling tape off the heads when play or record are not engaged.
This will lessen the tapes contact with fixed objects.
While one of the most easy and cheap ways to start is to push the lever on the right of the headblock pulling in the arms that keep the tape off the heads when winding (old style programme search when winding), this will mean more wear to the heads, but while the heads are less prone to pick up debris or scrape the surface it is actually just the slightly lesser of two evils - wear the heads or have the tape scrape the arms.
When I wind a fragile tape I either play at 38cm/s (15IPS) in the U-loop, or I let the tape go straight from supply to take-up reel and hold down the two upper tension arms, to engage the transport modes for fast forward or fast reverse.
-Mikkel