Both the M1 and M29 81mm mortar were used in VN. I don't know if the M29 had replaced the M1 completely that early in the war. I don't know what version 81mm mortar the 1CD had during the period of the film. Both types were used in the war though.
The big visual difference between the two is that the M29 has a round baseplate (the M1 is rectangular), and fins on the longer barrel. The M29 weighed a bit less and shot the same rounds about 400m farther.
The current M252 is a Brit mortar that weighs even less than the the M29 and has a much greater range.
Mortars are like anything that shoots. You shoot it too fast and it gets too hot. While a mortar doesn't have a "mechanism" per se, it could cook-off rounds, which would kil the gun crew, or at the least send the round off to land in the wrong place, neither of which is a good thing.
Ross