Broken Base: Enema of the State broke the band's fanbase in half, in large part because it made the band mega-stars.
Neighborhoods has those who are enthusiatic about the idea that they're incorporating elements of their various side projects into it, and those that hate it because it's "justAvAwith Mark".
Face of the Band: Subjective; both Tom and Mark sing an equal number of songs, with Mark being known for "Dammit" and "What's My Age Again" and Tom for "All the Small Things". Travis meanwhile is known mainly for his reality TV show and his near death experience.
Most older fans however, consider Mark to be the "true" face of the band however; in part because Mark is "more punk" than Tom, whose tendency towards the emo-sound (and aesthetics; mind you, he had an emo fringe long before the emo trend went big all over the world, with fringes and all!) alienated some fans.
Not to mention that all of their earlier singles (and as a result, videos) were written and sung by Mark ("M&Ms", "Dammit", "Josie" and "What's My Age Again"). It was only with "All the Small Things" that the tables were turned singles-wise (which is also video-wise). Album-wise, they tended to have opening and closing tracks written and sung by Tom most of the time, which hasn't changed so far.
Many people consider Travis to be the most famous (and talented) member.
Funny Moments: The between-song banter on the live album, The Mark, Tom & Travis Show, is so infectiously stupid they even go so far as to throw together a long string of these moments as a series of hidden tracks. Listening to them both throw out as many peepee jokes as humanly possible in one show (actually, two) is something to behold.
And speaking of infectiously stupid, the video for "All The Small Things" is a wildly immature parody of the boy band videos of the time.
Gannon Banned: Important tip: DO NOT EVER CALL THEM EMO AROUND ANY OF THEIR FANS.
Misaimed Fandom: The "All the Small Things" video wound up exposing the band to waves of squeeing teenage girls who didn't realize or care that they were making fun of boy bands with that video.
Tear Jerker: "Adam's Song" and "Stay Together For the Kids".
Not Now, as well.
They Changed It, Now It Sucks: The group's last album took them into an emo-sounding direction, which didn't go over well with fans.
"Neighborhoods", although less in a emo-sounding direction and more of a "let's take blink-182 and elements from all the other bands we did during the breakup, put 'em and a blender and see what comes out of it" kind of way. Putting the Darker and Edgier feel of the self-titled and the directions of +44 and AVA, it's hard to see how some people didn't see it coming. Or not.
Tom himself, according to many fans. YMMV whether these are legitimate concerns, kneejerk reactions to his attempting to grow as an artist, continued resentment towards his partially painkiller addiction induced Jerkass stint right before and halfway through the hiatus, or just plain complaining for the sake of complaining.
And then there is Enema of the State/Take Off Your Pants And Jacket, the albums that marked their mainstream breakthrough. Enema has its fans (with good reason), but a decent chunk of oldschool blink fans hate both (moreso Take Off Your Pants And Jacket)