1. In the bridge attack scene, Tom Cruise quickly assembles his G36 just in time to shoot down the drone that's coming in for a second pass at him, after missing the first time to annihilate his car. He looks over a large hole blown in the road, the only ground remaining obstructed by a flaming wreck, to see The Bad Guy about to escape onto a helicopter. He takes off on a short running start, tosses his gun, and barely clears the gap, sliding and catching the edge. While Tom Cruise...er...Ethan Hunt is known for performing many almost certainly impossible feats, is this one of them? Useful things to know are his velocity at takeoff and the distance of the gap. Tom Cruise claims he can run 17mph and while this is almost certainly not true, it's plausible for his character. As an athlete it is possible to reach maximum speed within 4-6 strides and he takes about 7. The gap is about the width of 7 tires, assuming they're about 26" in diameter that makes it 4.6m wide. In this past olympics, 11th place in the women's long jump was given to one Ivana Spanovic with a distance of 6.35m. Another thing to consider is that while Tom Cruise may occasionally act like a tank or some sort of invincible armored car, he doesn't behave like one in accelerating straight over drop-offs. His jump gives him a little more vertical lift as he crosses. Given this, the amount of acceleration he has, and as an adult male in good physical condition, it is possible that he would have made this jump.
2. Another question of physics comes up with the jump/swing scene. Tom Cruise is desperate to get his wife back, desperate enough to do some literal sketchy math and decide he can reach the top of his target building simply by swinging from a taller building next to it, effectively making all of Bad Guy's security measures useless. We're given all sorts of relevant information, such as his target building (B) is 162m, his swing point (A) 226m, and the buildings are separated by the strangely exact distance of 47.55m. The difference in height is 64m. With some basic trigonometry you find that to reach a cable in a straight line from the fulcrum point of building A to a point straight across on the roof of building B would require it to be 80m. Tom Cruise most likely calculated for it to be a little shorter so that he didn't become abstract window paint. The physics question remaining out of this would be: can he reach a high enough speed from his starting angle, when the rope first snaps taut after his jump, to carry him far and high enough to not simply fall short and slam back into building A? Important factors for this would be his speed, the distance along the path of the arc that the angle (about 130 degrees) creates, and possibly his mass? With some more math I found that the arc length is about 216m. At this point I'm fairly sure this turns into a 2D kinematics problem (hopefully for Tom Cruise's sake not a collision one) where you treat his initial freefall and the swing separately to calculate the speed, however attempting this I got straight up lost so I'll leave it as a posed question. To the inexperienced eye he appears to impossibly speed up in the second half of the arc on the upswing when they cut between shots but only physics can truly determine exactly how stupid desperate Tom Cruise was here.
3. The last scene I chose was the helicopter chase scene. They are escaping after a successful rescue mission of soon-to-be creepy-eyes-dead-lady, but are being pursued through a field of wind turbines by an Apache helicopter armed with among other things, heat-seeking missiles. After several close calls the pilot of Tom Cruise's helicopter decides to kill them all by flying through a turbine, just kidding, it's a tricky evasive maneuver and the Bad Guys fall right for it, flying through after them and not being able to perform a similar not-dying stunt. So the question is: can they really be that stupid or is there some typical movie trickery going on that makes the Bad Guys always lose? And the actual physics question is: at the velocity they were following at, and the timing of the blades, should the Apache helicopter also have made it through the turbine? Appropriate values to find would be the velocities of both helicopters, the distance through the turbine, and the speed of the blades. None of these are available or easily calculable in standard measurements so I will be using approximations. Up until this point, the Apache has been matching team TC's copter, never more than 2-3 seconds behind. The speed of the blades is approx. one rotation per second. The first helicopter takes exactly this second to fly through, the next blade actually looks like it should come down on the tip of the tail. The Apache, approaching the turbine at an identical velocity, takes almost three full seconds to pass through from the exact same point. The third blade crunches with a satisfying explosion directly into the middle of the helicopter. It's not possible for the helicopter to have slowed down that quickly from the speed they were pursuing at (Apache top speed is 182). If I had actual values to plug in I would find this clearly violates some kind of minorly super important stuff, like the basic laws of motion.