Continuity mistake: When Katniss meets Cinna, he has 4 earrings in his left ear and 2 in his right, so the last shot (when he says that Katniss "shouldn't be dressed up in some stupid costume") is clearly inverted. (00:29:25)
Continuity mistake: Katniss pulls Peeta up onto the top of the cornucopia and you see him, albeit briefly, kneeling on the top. Camera cuts and he is now back to hanging from the cornucopia, being attacked by the dogs again. (01:58:40)
Continuity mistake: When Haymitch is asking whats the hurry on the train, he has both hands up in the air (one with his glass in). Camera cuts to an angle behind Haymitch and his free hand, which should be visible in this shot, is not. (00:22:50)
Answer: I watched this scene multiple times on YouTube. There is definitely something moving that probably is not supposed to be seen. I'd agree with your assessment that it looks like a hand. Most likely a film crew member is crouched on the floor performing some technical function during the filming. Just what it is impossible to tell. You should submit it as a "movie mistake."
raywest ★