Continuity mistake: The tyres on the crotch rocket motorcycles they were riding kept changing from knobbly tyres to road slicks, back and forth depending on what terrain they were on. Easiest to see when Ethan skids on the road to avoid the white van - clear shot of slick tyres - then about 30 seconds later they're on the dirt, he skids into the old car and you can easily see that he's got off-road tyres front and back.
Continuity mistake: In the car chase scene with Nyah after they split and hit again and are spinning look at Ethan's car. The driver's side in the close ups was on the American side, then in the spin it is reversed to an English side. (It is a negative image - the license plate is reversed). The next image is back to normal.
Factual error: In the scene at the race track where they show the virus infecting and destroying cells in the blood stream, they clearly show that it is red blood cells being infected. Viruses, in order to replicate, require the cell's DNA replication machinery. However, mature red blood cells in the circulation no longer possess this machinery since they no longer have a nucleus or DNA. It would therefore be impossible for this virus to replicate.
Continuity mistake: In the scene where Hunt is chasing Nyah in the car, there is a part where he almost hits a gray car. When the camera shot comes from behind, we see a gravel road on the side with pine trees, but when it cuts immediately to an air shot, we see a concrete bridge-like road with no gravel for several feet ahead or behind. It does this throughout the scene.
Continuity mistake: Why did Hunt's team decide to use an outback location as their Sydney base? It looks like it's in the middle of the Nullabor, which ain't exactly a helicopter ride from Sydney. Come to think of it, there isn't much terrain like that anywhere within a several hundred kilometres of Sydney.
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)
Continuity mistake: In the scene where Nyah is walking up towards Ambrose's house, the wind is playing havoc with Nyah's hair and scarf. Throughout the scene, there are several shots of her where there is no wind, her hair is not moving and the scarf is perfectly placed (most noticeably when she steps off the boat onto the walkway).
Continuity mistake: In the rock climbing scene, just after Hunt does his flying jump, he falls, slides down a smooth rock face and grabs a hold at the last minute to stop him plummeting to his death. When he pulls back up, and over he grabs a hand hold on the smooth surface which wasn't there before. If you know what you are looking for, you will also see that it is a bolt on hold which has been attached to the rock face.