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.
Hate Dumb: The parts of the fanbase that claim the Robin character "ruined" Batman. Batman preceded Robin barely a year before the latter was created, and Batman's sales figures doubled when he was introduced. It's arguable that Batman as a character wouldn't have even survived The Interregnum without his trusty sidekick at his side.
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."
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.
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.
What The Hell, Costuming Department?: 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.