These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
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 enthusiastic 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". While Dogs Eating Dogs received the same concerns, the reaction has been more receptive than with Neighborhoods.
Ear Worm: Most of their songs. NA NA NA NA NA, NA NA NA NA NA~
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.
Important tip: DO NOT EVER CALL THEM EMO AROUND ANY OF THEIR FANS. blink makes this "important" distinction even more complicated by those not in the know by touringwithbands commonly pigeonholed as emo (in the Wangst, eyeliner, and tight pants sense), touring with actual emo bands, and actually counting emo bands as influences (emo in the "offshoot of DC hardcore punk" sense).
Jerkass Woobie: Tom, in spades. Despite acting all assholish to his band mates during the 2003-2004 tour and the sheer amount of crap he caused (which was pure accident, even he admit it was his fault), you can't help but feel bad for him: He missed his wife giving birth to his daughter, was rarely around, and simply wanted to take a break from the band to be with her, something Travis and Mark didn't wanna do at the time. Add to the fact he went on a severe painkiller addiction due to spine surgery and getting so much shit from other hardcore blink fans blaming him for the band's break up in 2005-2009, and then being accused of changing the band's sound, you can't help but wanna give him a hug.
Memetic Badass: Travis. Being considered one of the best drummers in recent memory, having a ridiculous amount of tattoos, surviving a plane crash, and recovering from multiple injuries including serious burns to drum again in full capacity despite DOCTORS saying he never would can do that. Definitely a Determinator.
Misaimed Fandom: Back in the day, 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.
No True Scotsman: They always had this reaction ever since their first album, but it really peaked with the release of Enema of the State.
"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 into consideration, it's hard to see how some people didn't see it coming.
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)