The ship also could have taken some heavy damage between films. We don't know the specifics of the run in with a bounty hunter Han mentions in ESB.

The amount of work Han and Chewie are doing on the Falcon on Hoth, (and the trouble just getting off the ground) hints at major repairs or modifications going on.

I don't think we ever see any rebel techs helping out with repairs, only a droid. Not enough manpower to go around, or does Han not trust anybody besides Chewie with his baby?

We do know he probably recently installed that neat little gun that takes out the snowtroopers. Unless it was busted in SW, it would have come in handy when departing Mos Eisley.