"The Emperor is not as forgiving as I am."

Wow, I didn't realize that statement was so literal.

Ah the wonders of the Prequel Trilogy messing up the Old Timey Filmstrips... Er... Original Trilogy. Sure we've had countless discussions of why Luke can't remember his "real mother" and Leia can, why Obi-Wan can't remember R2-D2, why Owen can't remember C-3PO, why Jedi move so much slower in the Original Trilogy, and why Jabba looks so different in Episode I and IV than Episode VI.

So let's get those out of the way first...
For those of you used to reading questions like these as seperate entries I've included sub-entry titles. As to avoid confusion. I prefer to get them all out of the way at once so people will stop asking me my opinion
Skip down to Entry 78E for the non-"Done to death" entry

Rive's Official Answers and Opinions on the Topics
that Have Been Done to Death!

Entry 78A: Why can't Luke remember his "real mother" and Leia can?

I chop this up to a mother and daughter bond being stronger at birth than a son and daughter. Or Leia was more force-sensitive thus giving her "Images and feelings" in her early years of her mother.
Of course the real answer is that the movie was out of running time and they couldn't have Padme go on the run with Leia for a few years.

Entry 78B: Why can't Obi-Wan remember R2?

Sure he can, but he knows R2 is smart enough to keep his yap shut about Anakin and he doesn't really know what's going on yet.
Of course the real answer is that it would have been really weird to have a scene with Obi-Wan chatting it up in the shadows with R2 about the good ol' days while Luke is asleep. (assuming Lucas planned for Obi-Wan and R2 to have a history together, which actually isn't unlikely in my opinion since his plan was for R2 and C3PO to be the "outside observers" of the entire story).

Entry 78C: Why can't Owen remember C3PO?

Mostly because even if he did recognize him he wouldn't do anything about it. He's immediately aware that 3PO doesn't remember him and Owen isn't exactly wanting to bring up anything about Anakin and his damn fool idealistic crusades.
Again the real answer here is a scene doesn't really fit in and this relationship was likely completely unplanned.

Entry 78D: Why do Jedi move slower in the Original Trilogy?

For this one I'd just stick with the real answer. Special effects weren't quite up to the speed they are today combined with the fact that Lucas instructed his actors to act as if Lightsabers were "Excalibur Heavy".
If you want an in-universe answer I'd have to say...
Obi-Wan was out of practice
Vader was still a bit apprehensive about fighting his former master
Luke was untrained
Vader didn't want to kill Luke

Entry 78E: Why does Jabba look different in X movie?

Because CGI artists are inconsistant with source work sometimes

Entry 78F: What was Vader thinking when he hired Boba Fett?!

Sure this was all fine and dandy before the prequels... But now Jango Fett was the reason Anakin and Padme ended up in the arena and almost got killed.

"Don't move Jedi!"

Why would he want to hire an exact clone of the same guy with the same armor even? It's even worse in the 2004 DVD's where Boba's formerly raspy voice has been replaced with Jango's accent. Wouldn't this bring back bad memories for the Sith Lord?
Of course the real answer to this one is that there was no such tie planned in the 80's, but why would Vader trust a man frightfully similar to the one who was hired to kill his love by his Sith predissesor Dooku in a sense of the movies alone, what was Vader thinking? Had he no anger left towards that armor and bounty hunters?
Vader was quite forgiving in any case, even if he chokes his Admirals at the drop of a hat.