Revealing mistake: When Ethan's pal is in the helicopter and Ethan is escaping on the motorbike he fires a grenade launcher at the car - he misses the first time, gets the car the second time, but you can clearly see the bridge is made of wood - where the car gets blown up there's a big concrete/steel plate to support the bridge. (01:38:30)
Revealing mistake: During the scene on the beach just after the collision of the two bikes we see Scott and Cruise flying together in a big hug, but if you see the short shot when the black bike starts to explode frame by frame you will actually see a lonely man with his arms wide open.
Revealing mistake: When the two cars chase Ethan, note the skid marks further up on the road from previous takes. A second later, the jeep makes a turn on that very same spot.
Revealing mistake: When Ethan's pal is in the helicopter and Ethan is escaping on the motorbike, he fires a grenade launcher at a gold ford Taurus driving across a bridge. When the grenade hits the car and the car explodes it flies into the air and off the side of the bridge. You can see as the car is falling from the bridge there's no engine or transmission in the car. It is only a shell.
Revealing mistake: When we see Ethan Hunt jump from the helicopter, you can see that it is not Tom Cruise but his stunt double.
Answer: Ethan did not want her to kill herself. Giving her a gun would allow her to do so.