The mud left on Simon's shoulder by the foreman slapping his back disappears soon after, despite his having had no opportunity to change or clean his jacket.
When Stitch points the pump shotgun in Mal's face it's already cocked, but it makes another cocking noise raising it up with 1 hand.
If Stitch really spent 4 years in that box, he'd be a physical wreck barely able to stand.
After Jayne does his 'speech' and his audience clap, those standing behind the other crew members are miming clapping very poorly (as there is dialogue presumably this is to get a clean audio track).
Simon's cup jumps away from his mouth while he's drinking with Kaylee.
That's a bad jump cut. His moving the cup from his mouth was cut in editing.
That's a bad jump cut. His moving the cup from his mouth was cut in editing.
When Simon is talking about the building of the Pyramids by the Egyptians, he references the slaves being used for the work and how they were given liquid bread to keep them from starving and not rising up. However research has shown that slaves weren't used to build the pyramids in Egypt. They were skilled laborers, paid well, given good housing and fed well. There were no slaves used because slaves were uneducated and lacked the skills needed to do the work.
At 14mins, the guy is strumming the guitar in a manner not consistent with the music style.