Broken Base: Bill Schulz's abrupt, mysterious departure and subsequent replacement by Joanne Nosuchinsky led to division among long-time fans. Most were heartbroken and angered that he didn't get a proper send-off; some stopped watching the show entirely; some were saddened but decided to give Joanne a chance; and some (mostly among the show's more rigidly conservative following who didn't appreciate Bill's blend of liberalism and oddball humor) were actively delighted to see him get a Hotter and Sexier replacement.
Crowning Moment of Heartwarming: The tribute episode to the late Andrew Breitbart, who made frequent appearances on the show and was a personal friend of the guys. Rather than being a sappy and somber look back, it was an entire episode of everyone who knew Breitbart fondly looking back and sharing stories, having a few laughs over the funnier ones, and playing clips of Breitbart's funnier moments on the show before each commercial break. It was quite possibly the most genuine tribute to someone who recently passed a TV show has ever done, and by the end of it, you'll be both sad Breitbart is gone, and sad you didn't know him.
Fridge Brilliance: Greg's character, oafish, racist, misogynistic, constantly getting the simplest of facts wrong, and possibly a self-hating homosexual, is the perfect deconstruction of what the typical liberal thinks everyone on Fox News is.
Ho Yay: Once an Episode. Seriously. If one was to take their jokes seriously, you'd think Greg and Andy were an old, married gay couple and Bill Schulz is the loosest gay man to ever live.
Older Than They Think: The show frequently plays strange YouTube videos as if they are relevant to the story being discussed. Doing so has caused some detractors to claim the show is ripping off Tosh.0, despite the fact that Red Eye predates Tosh.0 and has been doing the video gag for longer as well.
They Changed It, Now It Sucks: Let's put it this way: If you liked Red Eye's Conservative-Liberal-Libertarian-balance dynamic between Greg, Bill, and Andy...Bill's leaving and subsequent replacement by the more Libertarian/Conservative-leaning Joanne probably hurts part of the show's charm for you.
Also played with regarding Pinch, Bill's newspaper-Muppet. The paper used to have a very central role in the show—offering comments on the stories, having entire specials oriented around him. etc. He eventually was limited to a funny during-the-intro comment on what the New York Times has to offer in the day's issue...and then for a time disappeared altogether—until fans complained, emphasizing that he was a major Breakout Character. Greg brought him back for a time, but he still made sure to remark when he did that the joke about the character was getting pretty old as far as he was concerned.