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.
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.
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.