Deliberate mistake: When the Dragon Emperor is giving his Terracotta army the speech near the end, you see a shot that pans across the faces of several of his soldiers. A few shots later, this exact same shot is played in reverse. It is very easy to tell if you look at the way the camera moves up and down to catch the different faces.
Deliberate mistake: When Alex and Lin are secretly watching Rick and Evie being forced to open the Emperor's coffin at the museum, they are speaking to each other at normal volume. However, given how close they are to the bad-guys, there's absolutely, positively no way they wouldn't be heard. (Obviously it was done this way so that the audience could hear their dialogue, but it's still a mistake).
Deliberate mistake: There's a very strange editing error in the final fight between Rick and the Emperor. After the scene cuts to Alex waking up, it cuts back to the fight. The Emperor hits Rick with a right hook, and when the camera cuts to Rick reacting, his head understandably flops to the right. But then the Emperor hits Rick with another Right hook... and when the camera cuts to Rick's reaction, his head flops to the left, in complete defiance of physics.
Deliberate mistake: When the Dragon Emperor is controlling the elemental orbs in the final battle, Alex shoots them, surprising the Emperor, who turns and looks at him. Except if you pay attention, there's absolutely no way Alex would have been able to shoot the orbs from the angle he's at. He's standing directly behind the Emperor, so he would have had to have shot through him to hit the orbs. And you can see plain as day that the Emperor is not hit by any bullets. It's a cool visual, but it makes no sense.
Chosen answer: For one thing, just because two different years are shown does not mean that a full twelve months passed before they arrived in China. Also, travel to an undeveloped third-world country in the mid 20th century was not like it is today. There were no jet planes, much pre-planning and preparation would have to be done before departure, different modes of transportation would have to be arranged, and there would be many stops, delays, and transfers along the way. This could cumulatively take many months.
raywest ★