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.
Factual error: Near the end, Ethan Hunt and Sean Ambrose engage in a high-speed motorcycle chase that culminates with them crashing their motorcycles head-on. Just before the crash, both men leap off their bikes and their bodies collide in mid-air above the crash. However, if Hunt and Ambrose were racing towards each other at 40 mph (a conservative estimate), then the combined force of their bodies colliding would be equivalent to an 80 mph impact, which would pulverize their skeletons and kill both men instantly.
Factual error: The portrait of Semana Santa (Eastern) celebrations in Sevilla are absurd. Weird wooden constructions on fire (I guess it refers to Fallas, a celebration from Valencia and Alicante, around 400 miles away, in a tradition in which people burn cheap satirical and arty polystyrene sculptures with the arrival of Spring). Repetitive satanic hymns, fantasy castles, ritual drums, fireplaces and candles everywhere, effigies on sticks on flames, traditional clothes from somewhere in Central America mixed with San Fermín outfits and flutes (from Pamplona, over 600 miles away), frantic dances and women throwing flower petals over the crowd. I only miss some bulls dancing around in flamenco clothes while drinking sangría. The equivalent would be to portray a US festival in which Mickey Mouse rides a horse wearing a scary pumpkin mask while being carried by a leprechaun watching fireworks.
Continuity mistake: When Ethan kills Ambrose his head lays on a rock. A shot later, half a second afterwards from a wider angle, it's on the sand facing the opposite way. Then a shot later back to the first close-up and it's lying back on the rock.
Other mistake: Ambrose smacks a stone on Ethan's forehead. No blood nor even a bruise appears seconds later when Ethan is kicked in the face and we get a close-up of him.
Other mistake: Luther tells Ethan that he will only have 40 seconds for the louvres to remain open for him enter the ventilation shaft at Biocyte before the alarm goes off. But the warning message on Luther's computer says that the limit is 20 seconds. (01:06:30 - 01:09:10)
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.
Continuity mistake: At the end when the helicopter swings in front of the woman on the cliff, the damage to the left side of the helicopter is missing - bullet holes, broken glass etc.
Factual error: There are no direct flights from Sydney to Atlanta. Also, a 747 cannot fly the 9600 plus miles between the 2 cities. Even if it could the flight time would be more than 20 hours, probably 24. (00:02:30 - 00:03:00)
Answer: Ethan did not want her to kill herself. Giving her a gun would allow her to do so.