Microwave sparking

There are (at least) three possibilities:

1. Static electricity.
2. Current flow to something grounded
3. Capacitive flow.

Most everyone is familiar with static electricity I think. Sparking to a properly grounded electrical box is to be expected. Static charge can be built up and stored on your body in many way, like rolling acrylic wheels of a desk chair across the floor. Or walking on a carpet. After being discharged, if you don't build up another charge, then there is nothing to discharge, so you don't feel anything.

For there to be current flow, there would have to be a potential. It is possible (though unlikely) that the light switch is mis-wired and presents a potential to the screw. If you touch it while also touching something grounded like the desk, a land-line phone, etc. then an electrical path exists through you. If you are not grounded, like when you repeated touching the screw, there is nothing to feel.

A capacitive path is even less likely than the second possibility. I am only aware of it under high voltage situations, such as this video of a flying helicopter being bonded to high voltage. It is current flowing each a.c. cycle back and forth and stored in a conductive object. It stands to reason that if huge sparks occur at, say, 200,000 volts, that a small version could occur at 120 volts using your body as a capacitor. If you are sensitive enough, you might be able to feel it. However, if you use a less sensitive part of your body, then maybe you wouldn't. Electrical sensitivity could well vary millimeter by millimeter across a fingertip. This explanation also requires that there be an (erroneous) potential on the light switch screw.

If the second or third situations exist, there is a wiring fault, so it is good an electrician will be checking it.

Just thought of another one:

A fourth possibility is that there is a strong radio transmitter near by. The capacitance of your body is more of a factor at higher frequency. Maybe you would feel it sometimes but not other times because the transmitter is not continuously on. There isn't really much to do about it.

Buy a new microwave.

It sounds like your microwave door is pretty cattywampus. Microwaves are carefully engineered and undergo extensive testing to ensure radiation is kept in, and are typically not intended to be user serviceable. Even a very small leak could have serious health consequences over time. Finally, if you are able to replace a door, you still don't have the equipment to verify that there are no leaks. In short: it's not worth the risk!