In the first scene where Juan holds up the Stage Coach, one of the children in the bandit gang is holding a Spanish double action pistol, an Astra 400. If this movie were to take place in 1914, the Astra 400 model would not have been invented yet, as it was put into production in 1921.
The dynamite Sean hands Juan before the bank raid is several sticks in a bundle, with a single fuse and cap in the center, but when Juan dynamites the vault door, he uses two single sticks, individually fused and capped.
When the deserter is taken from the train to be executed along with two others the wall behind him is shot at and damaged on both sides of the deserter. The following close-up shot of the deserter getting shot in the back reveals no damage to the wall.
When Sean sets his machine gun back on its tripod after setting the charges, it is loaded with a section of belt with no more than (possibly) fifty cartridges; he is never seen to reload it, but fires many more shots than that.
Also, when he stops shooting, it is because the gun has run out of ammunition - we can clearly see the bitter end of the belt go through the action, leaving empty links hanging on the right side, and no belt at all on the left side. But in later shots there is a belt with unfired cartridges visible on that side - though it seems to change length between shots.
The goof items below may give away important plot points.
John's second flashback to his killing of Nolan in the Irish pub contains footage that does not match up to the first time we see this scene. Nolan's head is positioned differently in both versions of the flashback (in the first, his head remains in the same position, while in the second it is tilted at first before moving back to a neutral position), while the shot of John pulling his concealed gun out is also different (the gun's barrel is positioned closer to the left of the screen in the first flashback, but closer to the center in the second).