* Lack of clear protagonist, especially in TPM. This has been brought up by several critics. We don't get to see Anakin until half-way into the movie.
In the prequel-trilogy, the protagonist was an ordinary guy swept up in galactic events. He had human flaws, and we could feel for the guy. Then we saw him grow and mature. What was Anakin's story? First we stupid little kid, then in the next movie we see an annoying broody teenager, and in the last movie we see an annoying broody teenager yet again.
* Star Wars is supposed to be a roller-coaster ride, both physically and emotionally. Don't drag it out in the Galactic Senate (TPM) or make it overly dark (ROTS). There needs to be both light and the dark in the movie.
* Cringe-worthy moments type 1: Aliens are depicted as funny. Even aliens getting killed is depicted as comedy ... In the OT we did not see this until a little bit in Jabba's palace .. but we got more of it in the Special Edition, and then a truckload of this type of manure in TPM.
* Cringe-worthy moments type 2: Real bad dialogue/directing. The script needs more than one script-writer. Most of the most memorable moments and lines in the OT were not from GL but from several people who helped out with the script .. or even ad-libbed by the actors. ("You're lucky you don't taste very good", "I know"). We have seen from deleted scenes/alternate takes from the OT that not all lines came out right the first time either - shooting should not be rushed.
Some acting is wooden because of overuse of CGI combined with a lack of direction. Several actors have said that they really hated having to work alone in front of a green-screen, and it shows in the result - the same actors' performances are not good in those scenes, and these are well-known classic actors with a good reputation.
* Bad female characters. In the OT, Leia is not only beautiful but she kicks ass, and we love her for it. She is the only woman we see much of, but she is a role-model for girls. She is strong, takes charge, challenges the men and she keeps her poise even when she has been taken as a slave. In the PT, Padmé can shoot droids and lead her kingdom of Naboo, but then she turns into a total wuss when she falls in love and in ROTS she has been transformed into something horrible. The OT got widely criticised for having only one leading woman, but there is still only one woman in the PT, except for the few who are practically extras because they don't say anything of value. If you want to attract female Star Wars fans, you can not do it with Padmé's wardrobe alone. The Sequel-trilogy needs strong female characters, and more than one.
* Pet peeve of many: Too much Tatooine. It is a backwater planet on the outer rim, far from the major events. People don't want to revisit the same boring old place, they want to see more of the Star Wars galaxy.