When Furiosa is cutting off her hair to make the wig, the tattooed stars on her forearm are gone.
During the Mortifiers' raid on the War Rig, the short hose changes positions in Furiosa's mouth: when the Black Thumb first hands it to her she clenches it between her teeth at one end (her left). The next two times she is shown, diffusing the dynamite and then climbing forward to fix the fuel leak, it's held right in the middle.
While Dementus' nipples were removed during his first in-person encounter with Immortan Joe. His nipples were magically back during the last scene where he was turned into a tree.
When Furiosa and jack are ambushed in the bullet farm. The pinned down car at the gate seems to come and go in between scenes.
(At around 1:14:00) As the camera approaches the back of the War Rig, the rear poppy-knocker hatch is open on top. Quick-cut to the small Warboy opening the rear hatch, which is suddenly closed.
Shooting a gas can with a bullet will not make it blow up, this is one of the most common Hollywood firearms mistakes. In order for the gas to ignite a spark would need to be made, nearly all bullets have a copper jacket and a lead core, neither of which makes a spark when hitting metal.
When Mary is chasing the men who took Furiosa she makes some shots that are rather impossible, shots that even an experienced Navy SEAL or Army Ranger sniper couldn't make (using the same gun anyways). The bikers she is shooting at (when they are approaching their camp) look to be well over 500 yards distant, the people in the camp are smaller than her crosshairs which makes them more like 1,000 yards. She has an SKS, it is a medium powered rifle and has a maximum effective range of about 440 yards (400 meters), after that the bullet starts rapidly dropping. A skilled marksman could probably hit targets beyond 500 yards, but only a stationary one with little to no wind. The speed the bikers are moving at, combined with the strong crosswind cutting across that valley, would make a shot at that distance with that rifle nearly impossible.
The revolver Dementus carries is a replica of a black powder revolver called a LeMat invented by a French gunsmith in 1856. It is rather unique because in addition to firing regular bullets it had a single shot barrel that fired buckshot, like a shotgun. But this revolver, like all guns from that era, is loaded via the muzzle, it doesn't use cartridges or shells. So Furiosa loading a shotshell into the bottom barrel is wrong, shells wouldn't fit or fire in this kind of gun. Especially since it appears she uses one of the shells from her sawed-off double barrel 12 gauge, which is too large. The LeMat had two models, one fired .42 caliber bullets and had a 20 gauge buckshot barrel, the other fired .36 bullets and a 16 gauge barrel, both are smaller than a 12 gauge.
When Jack and Furiosa are entering Gastown around the 83min mark, the hinges of the main gate squeak as they open, yet the entire facility is literally surrounded by a moat of crude oil, a few drops of which would stop the squeaking.