I don't think there's any direct contradiction between how Simon said he got River out in the series and what we saw in the movie. He simply omitted the fact that he was the one that went in after her while those "others" he paid to help him are the ones that got him out. In fact we see in the movie a ship come and hoist them out of that shaft and there's no way he could have just walked in there on his own, it's clear that he had a considerable amount of help.
As for Mal's character, he's clearly slid back into a similar rut he was in during the pilot, thanks mostly the the departure of Inara and the increasing pressure of keeping his ship in the air. As the movie goes on things just get worse (specifically the wholesale slaughter of just about every friend and ally he had left), so he's hardly going to cheer up along the way. Nevertheless there are a few moments of levity, so it's still the same Mal.
Here is a script excerpt from 'Serenity' (the pilot, not the film) that concerns Simon's explanation of why River was in that box:
Money. And luck -- for two years I couldn't get near her, but I was contacted by some men, some underground movement. They said she was in danger, that the government was playing with her brain. If I funded them they could sneak her out in cryo. Get her to Boros and from there, I could take her... wherever.
In the movie, as previously stated, Simon is directly
involved in River's escape, which, as shown by the above excerpt, is in direct contradiction of what was established in the 2-hour pilot. It is also slightly contradictory to his character development throughout the early episodes of the series, although not to any real detrimental degree.