I've also never seen the original series - maybe I saw a re-run at some point - so I have no reference point. It's tough to make a contemporary film that is popular with the purists, and if this missed it, fair enough.
Watching the movie right now, I think the aspects I loved about it are that it is generally a fun movie, and the comic bickering. Whether it be between Agent 86 (Steve Carell's Max) and Agent 99 (Anne Hathaway), or Agent 23 and Larabee - there's a continual jibing dialogue laced with dry sarcasm, often quickly descending to a petty level at odds with the supposed importance of the situation. Verbal combat interspersed with gems like "The cone's the shizzle" or "Oh look, a box of kittens, I'll punch Max in the face", make this movie.
I enjoyed this movie as much as I enjoyed Airplane, The Naked Gun, and Austin Powers. Those are also spoofs of genres of films, and they're generally accepted to have worked - perhaps making a remake of a spoof is harder?
Combined with some well-judged slapstick, again reducing these top-tier operatives to a group of children - this is a fun, enjoyable movie. It exudes a warmth that makes me like to think that the cast had fun making it, but even if they didn't, I had fun watching it.