Revealing mistake: When the "Alien" is dancing along the bar, it kicks its legs. As it dances past Barf and Lone Starr in close up, its legs are stationary and the whole model is bouncing. On cut back to its disappearance through the "stage door", its legs are kicking again. This also applies to the other animations of the "Alien." You can also see the 'stick' that it is attached to, along with the hole cut in the bar to accommodate the stick.
Revealing mistake: When Pizza the Hutt is telling our heroes that they owe him money, watch his mouth. You can see the actor's real mouth appear a couple of times through the whole speech. The actor's chin is covered in the special effect pizza stuff, but you can still see his very human mouth every so often through this segment.