The ones in ANH that I have noticed are (for me) pretty hilarious. Like the bouncing Stormtrooper. When the Stormtroopers rush into docking bay 94 watch the scene closely. Han takes a couple of shots and at one point hits the archway and it explodes. At the same time one of the Stormtroopers colapses to his knees and then falls on his face. This is done in a long shot. Then in the close up of the Stormtroopers, the same soldier again falls to his knees and then on his face. Finally, as Han runs up the ramp, there is another long shot of the Stromtroopers and for the third time the same soldier does his thing. The only logical conclusion that I can reach is that this guy's uniforms must be made of rubber.
The circling Jawa is another good one. As Luke and 3PO are walking away after purchasing R5-D4 and C-3PO, R2 tries to sneak away. In the long shot of R2, a Jawa runs in front of him. Then just before R2 is stunned by the cheif Jawa, there is a close up of R2 and that same Jawa runs in front of him again. I believe it happens a third time, but I can't be sure. I'm sure everyone has noticed that when Uncle Owen says, 'What about that blue one? We'll take that one,' and thye show a side close up of R2, you can clearly see R5-D4 still sitting next to him. Impossible since R5-D4 is standing in front of Luke and 3PO.
Vader talking to Tarkin and his hands are moving but there is no dialogue.
Inside the sandcrawler you can see through R2's eye and see Kenny Baker inside.
During the battle of Yavin, you can see Vader's eyes or rather Dave Prowse's eyes through the mask.
The cardboard soldies during the awards ceremony.
Ben's lightsaber looses its color on a couple of instances during his duel with Vader and you can clearly see the sword (or fencing foil).
Has anyone noticed anything else from ANH? It took me years of watching ANH to find a mistake. Finally in 87, I noticed the first mistake. It was R5-D4 still standing next to R2 after the droid had exploded.
As for Empire and Jedi, I can't recall any at the moment so I'll let everyone else fill me in on those.