"Watched them get married" vs "watched them getting married"

It's largely a matter of stylistic choice. There can sometimes be a nuance of meaning involved - for example...

• I watched him hit the man

• I watched him hitting the man

...where the second one implies multiple blows more strongly than the first.

Feasibly a case can be made for saying "I watched him light the fire" attaches more importance to the fact that an act was performed (with the implication that the fire having been lit is important later). In contrast to "I watched him lighting the fire", which might be said to concentrate on the ongoing performance of the act (with the implication that the process itself is "interesting"). Any such distinction is tenuous at best, and would really be better discussed on writers.se