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.
The Robin identity in general. Some people think the very idea of a brightly-colored minor running around and fighting criminals is ridiculous. Others consider it a Necessary Weasel to keep Batman from getting too grimdark. Others invoke the Grandfather Clause and say that whether it makes sense or not, it's part of comics tradition and too late to change.
Jason Todd. Either he's a Woobie who's just misunderstood, or a murderous asshole who taints the Robin legacy. The fact that his characterization is inconsistent and heavily dependent on the writer (is he an Anti-Hero, an Anti-Villain or a straight up villain?) doesn't help matters.
Damian Wayne. Either he's a Woobie who just needs someone to believe in him (hello there, Dick) or a horrible character that only gets to be Robin because of his last name.
Narm: Tim Drake's identity of Red Robin can be hard to take seriously for readers familiar with the restaurant chain.
Never Live It Down: Dick and Jason for the shorts and pixie boots, and Jason for dying and being the 'angry Robin'.
Tim for his angst, and his own costume choices, going from "Condom Head" to the "Swan Queen."
Robin in general, gets a lot of crap for supposedly being a Distressed Dude. While Dick played this role straight a lot in the 60s series and Schumaker films, generally Batman was captured with him, and in the comics themselves Dick then went on to found the Teen Titans and become The Heart of the entire DCU as Nightwing. As noted in True Art Is Angsty, some people seem to think that Robin cannot work in live action, even if they're willing to admit he could work seriously in animated or comic form (which leads to some form of Animation Age Ghetto mentalities).
Replacement Scrappy: Pretty much every legacy to take on the role for either the one before them, or for Dick Grayson himself. Jason got so much vitriol it lead to killing him off, Steph's still not forgiven by some hardcore Robin fans for not 'earning' the role, and a big part of the reason Damian is seen as such a Creator's Pet is because of this. Tim seems to be the only one not to be hated due to being a Hypercompetent SidekickKid Hero who helped shrug off the reputation of being a Distressed Dude, but even there, there is some fans who seem to see Dick Grayson as the only Robin and so hate him and the legacy for this reason (though, these are rare), and his New 52 version is pretty much this for his Post-Crisis version.
Rescued from the Scrappy Heap: Jason Todd, to a degree. His Red Hood persona seems to have gained quite a few fans, although he is still the biggest Base Breaker Robin.
Damian Wayne, thanks to some nice character development and his relationship with Bruce and Dick, has become less of a Base Breaker (although, like Jason, he still is one).
However, various factors have come to light which muddle the issue. Many readers at the time were children, and couldn't make the not-so-cheap phone call. Also, in an interview, Dennis O'Neil recalls hearing a rumour that one guy had his computer call the number to have Jason killed multiple times. However, a few people also thought the vote was for Dick Grayson, and voted to keep Robin alive, thinking it was him, and that is not a rumour.
They Changed It, Now It Sucks: The New52's origin for Tim Drake is heavily critized by many fans. Pre-boot, he was an intelligent, non-athletic nice guy and Audience Surrogate who had the most "normal" upbringing of all the Robins and became Robin because he realised how important it was for Batman to have a Robin. In the New52 continuity, he's an arrogant, friendless gymnast. He has never been "Robin" and only ever been "Red Robin", became Batman's sidekick because he wanted a challenge and his last name isn't really Drake.
In-Universe, Tim was treated this way after he lost his father, his girlfriend Stephanie, and his best friend, Superboy, all in rapid succession.
True Art Is Angsty: A part of the reason for so much stigma against Robin outside of cartoons and comics; the idea of Batman, a dark and brooding loner, taking on a protogé who dresses in a campy brightly coloured costume is seen as such an ill-fitting idea that some believe that Robin simply cannot work on film, and its not helped by the only time he got a 'serious' film adaptation was the Joel Schumaker films, Batman Forever and Batman & Robin, which didn't do well for his image, leading both Christian Bale and Christopher Nolan swearing against including him in their films. It should be noted that in those films and the classic Adam West 60s Batman show, Robin wasn't any worse than Batman in how he was depicted, so blaming him for it is pretty unfair.
Dick Grayson's New 52 Robin outfit. Poor colour balance and unnecessary line work aside (that's the trend with the New 52), for some reason DC decided that a red arrow pointing towards his crotch was necessary, as if a thong would look good. Notable since Cyclops seemed to copy Nightwing's outfit when he was powered by the Phoenix Force, particularly Dick's red bird, and it seems Dick is returning the favour by taking Phoenix!Cyke's thong-arrow-thing.
While it gets a pass generally for Grandfather Clause reasons, the classic Robin outfit is seen as this for many people. Of course, the biggest issue is the uncovered legs, and one could make the argument that many of the people who deride it often have no problem with female characters baring the look (infact, Gender Bender female Robin costumes are pretty popular in some parts for being Fetish Fuel), which leads to some Double Standard issues.
Inverted/averted with the Batman Arkham Series take on the Robin costume. Both Tim's and Dick's outfits, as shown in Arkham City and Arkham Origins respectfully, are generally well received as they could easily work as film versions of the outfits.