Other mistake: When the camera changes shot to the security feed for the first time in River's bar brawl scene, you can see, on the top right, Jayne and Mal sitting down with Fanty and Mingo and the Dancer preparing to block the camera's view. This is before the gang have even stepped into the bar.
Other mistake: When the Assassin is pulling up the identity and history of Malcolm Reynolds, based upon the security video of River's bar fight, it shows that he was a volunteer for the rebellion forces, but lists his rank as Captain, while we know from several instances on the Firefly series that he was a Sergeant.
Answer: Here it is on YouTube: http://www.youtube.com/watch?v=BLF5J7rFjhs.
Myridon