Since this was the second viewing, we thought we would look for some of the subtleties and sequel issues in the move (there are whole web sites dedicated to this, so take these as observations from average fans, and not Comic-Book-Store-Guy fanatics). WARNING: Contains Spoilers:
Anakin Created by the Dark Side? - During the chat between Palpatine and Anakin during the opera-dance-swimming-thingy, Palpatine relates the story of (presumably his own) Sith master who could "manipulate mitochlorians to create life", which we learn in SW I is how Anakin was conceived. So was Anakin part of a long-rage plot by the Dark Side?
"Love is Blind" Scene Not That Bad - A lot of criticism has been thrown around about the scene where Anakin and Padme talk about "you're so beautiful", etc., and how audiences laughed. Watching this the second time I thought it was supposed to be funny since the two were bantering; basically joking around with each other by playing with words and using hackneyed phrases. Anyone who has been in a long-term relationship might understand how this sort of stuff really happens. The "I'm pregnant" scene still gets a raspberry, however.
This is Your Father's Lightsaber, Sort Of - After the Obi-wan/Vader fight, Obi-wan picks up Vader's lightsaber. This was necessary since in SW IV, he gives Luke his "father's lightsaber". The only problem here is that when they fought, Vader's blade was (dark side) red, but when Luke turns it on, it is (light-side) blue. I don't know the "official" doctrine on light-sabers, but based on the SW video games I've played, the color is controlled by crystals, so I guess we have to assume Obi-wan changed it out.
Dead and Pregnant? - I didn't notice this, but Mrs. Director says Padme looks pregnant during her funeral, assumingly so any Empire spies in the audience will confirm that the child died with her. I have no idea if this is physiologically accurate or not in real life.
Politics Impossible to Figure Out - Mrs. Director and I tried to figure out the politics over cocktails afterwards, but as Poliblog noted, they just don't make sense. Padme laments "this is how democracies die", but her own husband was born into slavery. Like much of the plot, this is one area where you have to put your brain on hold and go with the flow. This is supposed to be a space opera and not anything with deep political meaning.
My, How You've Aged - This is technically an issue with the actors and not the plot. At the beginning of SW IV, Luke is on the verge of manhood, so around 18 or so. When Obi-wan drops him off at the end of this movie, he (Obi-wan, not Luke) looks like, well, Ewan McGregor (34 this year). In SW IV, Obi-wan looks like Alec Guinness (about 63 when Star Wars was released). Similarly, the actress playing Beru in this movie is a young, attractive woman (played by a 22 year old), but in SW IV she could charitably be described as "middle aged". Maybe that desert sun prematurely ages people?
Were the Wookies Really Necessary? - Not a plot hole, but just a comment that the whole Wookie thing seemed unnecessary. It seemed to be put in there just to put Chewbacca in the story, but that leaves people wondering how he went from being a leader on his planet to an outcast smuggler 18 years later.
I'm sure I'll come up with a few more when the video comes out, but I promise no more postings. If you're that curious there are tons of sites dedicated to this sort of thing.