My son replaced the sillcock valve easily enough, using plumber's tape at the connections, but there is a tiny drip from the adapter and now the water shut-off valve. The home was built in 1990.
Could this be caused by over-tightening the valve?
Yes you can definitely over tighten threaded connections. The typical rule of thumb is to hand tighten, then tighten a quarter-turn with a wrench. If you still have leaks, repeat the quarter turn until the leak stops.
Also make sure that on threaded connections that you use Teflon tape or pipe dope. Do not use this on compression fittings.