Don't do it.
Microwaves, while safe, emit a significant radiation that is controlled, in part, by a carefully designed door interlock system. If it is compromised, there is a risk of radiation leakage.
You don't fix microwave doors, you send it back for them to fix or you replace the entire unit.
Period.
SUPPLEMENT
The World Health Organization (WHO) has this to say about microwave oven safety.
Microwave safety: The design of microwave ovens ensures that the microwaves are contained within the oven and can only be present when the oven is switched on and the door is shut. Leakage around and through the glass door is limited by design to a level well below that recommended by international standards. However, microwave leakage could still occur around damaged, dirty or modified microwave ovens. It is therefore important that the oven is maintained in good condition. Users should check that the door closes properly and that the safety interlock devices, fitted to the door to prevent microwaves from being generated while it is open, work correctly. The door seals should be kept clean and there should be no visible signs of damage to the seals or the outer casing of the oven. If any faults are found or parts of the oven are damaged, it should not be used until it has been repaired by an appropriately qualified service engineer [emphasis added].
The US Food and Drug Administration (FDA) says this
Checking For Leakage: There is little cause for concern about excess microwaves leaking from ovens unless the door hinges, latch, or seals are damaged. If you suspect a problem, contact the oven manufacturer, a microwave oven service organization, your state health department, or the closest FDA office [emphasis added].
The problem described is not just tightening a screw or putting a seal back in its track. The door is misaligned and poses a risk. Trying to realign and weld parts of the safety system seems very ill-advised.
Most microwave ovens will generate arcs and sparks inside their cavity if they are run with an insufficient load, or no load whatsoever. The high-frequency content from these arcs is being coupled (likely capacitively) through the HV transformer section of your microwave onto the AC line, where the AFCI can then see it and proceed to freak out, thinking the arcing is actually an AC mains arc, not a microwave cavity arc.
Suggestion: throw a coffee mug of water in with the slice of pizza. This does the same thing as Keshlam's sacrificial bread slice -- i.e. provides more load to absorb the microwaves instead of letting them bounce around the cavity until they arc, just without having to waste a slice of bread.
Best Answer
Simply wave a fluorescent tube around the micro when on, any leaks will illuminate the tube. Of course, if you find something, get it replaced ASAP. The radiation is not the cancer-causing ionizing radiation, but it can easily damage the blood vessels in your eyes and cause other minor burns.
EDIT: I should mention that skin burns, even minor ones, raise your lifetime risk of skin cancer.