"Yes, I was once a Jedi knight ... the same as your father."
"He was the best starpilot in the galaxy ... and a cunning warrior."
"And he was a good friend"
In AotC, Anakin and Obi-Wan spend over half the movie separated from one another. We're supposed to buy into their relationship and sympathize with their conflict, but Lucas doesn't make the effort to develop their relationship beyond the most superficial level. The characters are simply presented as cut-outs - "Anakin is the whiny teen who thinks he's better than everyone else," and "Obi-Wan is the authoritative father who always thinks he knows best". We're fed this information in the first fifteen minutes of the movie and their relationship is never developed any further than that. And instead of having scenes where Anakin and Obi-Wan show their feelings through action, Lucas simply writes expository dialogue where they describe their feelings. These are fundamental screenwriting mistakes, providing proof Lucas has lost the touch (if he ever had it to begin with. In the past he always got help from others). Compare AotC to the rhyming ESB, where Luke spends over half the movie separated from Leia and Han. Luke's relationship to Leia and Han isn't integral to his development and his subplot whereas Anakin's relationship to Obi-Wan is. By creating these films on auto-pilot, Lucas has destroyed all depth of characterization.
The end battle between Obi-Wan and Anakin in RotS would of been much more gripping if we saw two "very good friends" battling, rather than what audience got to see, an acquaintance rather than a good friendship.
Another major problem is the transition from TPM to AotC. In TPM, toddler Anakin develops a relationship with Qui-Gonn Jinn. In AotC, adolescent Anakin is apprenticed to Obi-Wan. Lucas, by completely elliding the development of the relationship between Anakin and Obi-Wan, leaves the audience in the lurch. As a result, any investment in the characters formed in the first movie is squandered.
The problem is that Lucas is a slave to style when story should come first. By style I'm referring to Lucas's insistance on retaining an objective kind of time in Star Wars, where the films are edited to resemble real time (no big jumps in timeframe or alterations in the pace). Better would have been to introduce young Anakin in TPM and then show his growth and development into adolescence and apprenticeship via a montage. This would have enabled Lucas to present Anakin's growth in a visual manner, maintaining continuity, while showing the Jedi training methods that fans are interested in. It would also allow the viewers to compare Anakin's prodigious talents to his peers (who would be seen training beside him), showing us why Anakin appears to be the chosen one (instead of telling us through some stupid prophecy). Again, compare the transition between ANH and ESB to the transition between TPM and AotC. In ESB, Luke is a little older, but still played by the same actor, and he still retains the same character traits. Whereas Anakin has gone from being a toddler to being a teen, and from being a precocious boy to being a whiny and annoying teen. The audience does not get to see the development, and so is left cold and unsympathetic to the primary protagonist.