1) Lack of a strong villain. Unlike the OT, where Vader was the man to fear for the entire trilogy, the PT had no strong villain figure. Palpatine just sat in the background scheming and plotting never really doing anything evil until halfway through RotS. Every time we meet a strong villain character (Maul, Dooku, Grevious), they die very quickly and we never get to a point where they could be recognized and feared. If Lucas had let Maul escape after he killed Qui-Gon instead of being killed, then had him lead the seperatists in Episode II before finally being killed by Obi-Wan in Episode III, things would have been a lot better on that front. Or perhaps introducing Darth Tyranus in TPM (Which would have been cool, since he trained Qui-Gon).2) Lack of a strong group dynamic. In the OT, Luke, Leia, Han, Chewie, Lando, R2 and Threepio all knew and interacted with each other in various ways. TPM was able to capture this feeling with Qui-Gon, Obi-Wan, Anakin, Padme, R2 and Jar Jar, but it completely dissapeared after that. It became a "Chain" as opposed to a "net." Padme interacted only with Anakin (which made her seem somewhat like a 5th wheel), who interacted only with her and Obi-Wan, who interacted only with Anakin and Yoda/Mace. See? No group, there. It really hurt the feel and cohesion of the movie. Instead of watching seperate parts of one story that weaved through each other from time to time, it felt like we were watching several completely seperate stories that coalesced into one at the very end.
3) Lack of a strong lead actor and lead actress. Covered above.
4) Lack of beliavability. Anakin's fall to the dark side was WAAAY too rushed. It just felt like "OK, just killed my master in a spur of the moment event. Guess I'm evil now, so I'll go and slaughter everyone I ever knew and loved. I'll even kill the kids so I seem even more evil. Oh... maybe I should be a bit remorseful too, so I guess I'll go off and cry for a bit."
5) Lack of strong space battles. TPM's space battle wasn't bad, but it didn't capture the epic feeling of either of the Death Star Battles. RotS's space scene was ho-hum at best. The whole thing felt like it was on rails a la Starfox.
6) Narrow-view of the Star Wars universe. Again, aside from TPM, the entire series is focused almost entirely on the Jedi and their way of life. In the OT, we had a smuggler, a rebel leader, a Jedi and an business man. Each of these gave us a seperate view of the galaxy. In the PT, it really just felt like you were following an upper-class noble around and had no chance to get a feel for some of the "cooler" parts of the galaxy like the Mos Eisley cantina.
7) We knew the story already. This really couldn't be helped, but it did hurt the movies.
8) Lacked the epic feeling of the OT. In the Battle of Yavin, the fate of the Rebellion was in the hands of a handful of rebel pilots hurtling towards the seemingly-unstoppable might of the Death Star. At the Battle of Endor, the destiny of the entire Galaxy sat on a razors edge as the forces of good and evil clashed in a final battle of titanic proportions. There were no such instances in the PT. Just a sudden takeover by the Empire and a slaughter of the Jedi. Maybe if the Republic had at least put up a fight before it got taken over, things would have been better.