You're right about the error where they cut to the outside and he's shooting a M14, then the cut inside and back out and he's shooting an M16, then back inside the chopper and back to him and he's shooting the M14 again. When they both got off the plane it's clear that they each touched down with one rifle each, one M16 and one M14. So it's definitely a continuity error.
I noticed it the first time I watched it. There are some other errors too, but I'm not sure if they're correct or not. In the scene where the hummer pulls up over the dune and heads to the range where the Rangers are shooting, the barrel wobbles on the mounted machine gun. To me it looks like normal movement from coming over the dune at speed, but on imbd.org it says that it looks like the gun is just a rubber prop. Having some experience in that area, it looks a bit too realistic and detailed to be a rubber prop.
Also in the beginning where they shoot through the hood of the jeep, it looks like he uses a M14 for the shot and then has a M16 when he's on the ground, but when he takes a shot in the plane the guy next to him has an M16 and they do look similar. So I'm thinking that one is not a true error either.
If you watch some of the scenes where they are stalking through the alleys, you can see the fake walls move.
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