ANY movie mistakes... whoa, there are a ton of them. You can finds lists of hundreds of them all over the internet (usually responded to by somebody saying how they aren't REALLY mistakes, because somehow... blah blah blah nonsense sci fi rationalization retcons, hehe).
Probably the classic is the taller Stormtrooper banging his head on the low door in the original Star Wars (which Lucas added a "bong" sound effect to in 2004 because it had become so famous by then). The first time I noticed it (which was years after I'd first seen the movie) I cracked up, and could watch it on a loop!
Another mistake is where Obi-Wan and Luke are talking before they go into the Mos Eisley cantina, and an (African American) extra walks past the camera behind them as they are talking FOUR TIMES. I bet somewhere somebody is writing a novel or there's a comic book short about these "four identical brothers" who were on their way to the cantina on that day or something (and how they gloriously died fighting the Empire or something).
There are tons of mistakes in the original Star Wars and the sequels, just from special effects errors, editing errors, etc. there are also science errors in every movie. The Prequels have their own internal errors and then continuity glitches with the original movies, etc.
Some people get mad when you point out mistakes and try to "explain them away" with suspension of disbelief (you know like saying "well Han says parsecs but he means you have to fly the kessel run past black holes that distort time and space") but you know that we're talking about the movie as a story itself, not as some part of a research project where you have every script, novel, comic book, video game, and official fan page explaining every minute detail of the movie for you (with explanations invented sometimes years after the movie was made, by people with way too much time on their hands).
Probably the most annoying continuity error for me in the Prequels is where Padme dies in childbirth, yet in Return of the Jedi we're lead to believe that Leia (who doesn't know the Force) remembers her "real mother" somehow but Luke (who is practically a Jedi Knight) doesn't. And I know people try to say that Leia saw her mom through the Force, but then we must wonder why Luke wasn't able to do that, and if Leia had such a special gift, and why nobody noticed it (Vader didn't get suspicious even though he was interrogating her on the death star, but Luke he only saw from a distance and sensed the force right away; Obi-Wan never thought to train her even though she was already an important rebel leader and being chased by Vader, etc). That's not so much a "favorite" as one that stands out to me as a very annoying and avoidable mistake. It's like he just really wanted to give Natalie Portman's character a death scene in the third prequel and didn't care about the consequences. At least he could have had Yoda look into the future and see her dying years later in hiding on Alderaan with a little girl by her side or something, then looking sad to himself and it wouldn't have broken previously established continuity.
Sorry to get off topic... you really wanted to know about mistakes IN the OT.