Always happens after I watch one of the original trilogy films again. In this case it was ROTJ.
1) The Emperor and (particularly) Vader keep assuming it was Obi-Wan who taught Luke the ways of the Force. Clearly, neither of them knew of Yoda's continued existence. Yet, they both _knew_ Yoda as the head of the Jedi Council at one point. So how did they account for (or not account for) Yoda's demise/existence? Perhaps this will be explained in Episode III, as well as Obi-Wan's escape to Tatooine.
2) Who was Palpatine/Sidious' Sith master? Clearly, he apprenticed under someone before ascending to the Sith Master position he holds in Episode I. Also, if Palpatine was so strong in the Force (as he must have been to accomplish what he did with the Dark Side), how does he go undetected as Anakin did (referenced by Qui-Gon in Episode I in conversation with Shmi)? If he was a Senator from Naboo, he probably was a citizen of Naboo from birth. Surely, Naboo was within the Republic's main cognizance and the within the ability of the Jedi Council (or whomever detects the presence of the Force in little kids) to find and identify. Is the Dark Side genetic and Palpatine just knew he was bad from the start so he blinded the Jedi Council?
3) At the end of ROTJ

E, it looks as if Mos Eisley is shown partying at the demise of the Empire. Yet in TPM, we learned the Republic had little presence out there. Did that change with the onset of the Empire? It seems to me even the Empire wasn't that involved in Tatooine, even if the stormtroopers were there in ANH under Vader's orders looking for the stolen data tapes/droids. Also, since the Empire/Emperor/Vader never seemed to be able to realize Luke was living there ... I just don't think Mos Eisley (or Mos Espa, for that matter) would have been partying like it was 1999 at the demise of the Empire.
Just food for thought.