Arc Fatigue: For a number of people. The main reason was that Trinity War, an event DC had been shilling for over a year, turned out to merely be a lead-in to Forever Evil. Add in a generally sluggish pace magnified by the main series being delayed - the 7th issue came three months after the 6th - and you've got readers making a lot of jokes about the title.
The appearance of Sinestro in promotional art didn't go over too well with Green Lantern fans, who were hoping DC would leave the character alone after the ending of Geoff Johns' run on the series closed by giving Sinestro an effective send-off. Of course, there are fans who are quite happy to see Johns writing Sinestro again, also along with the fact that it closes up character threads from Wrath of the First Lantern - as Volthoom is historically Power Ring's mentor.
Inversely, some fans are upset that despite being a major event focusing on DC's villains, The Joker is absent, while others are happy DC's finally leaving him alone, since Death of the Family happened a few months prior and especially considering The Joker himself was a Base-Breaking Character in said arc, where some were okay with him and some think The New 52 turned him into a Narmtastic Villain Sue. Though some fans argued that the main reason Joker should be involved was so they could give him Character Rerailment from this.
Nightwing's unmasking was, as you'd expect, a cause of this. In part, because the New 52 hasn't established that Nightwing being unmasked would have as big an effect on the DC Universe as it would have done before the reboot, due to his lack of interaction with non-Bat Family members post-reboot, whereas before the reboot Nightwing was arguably The Heart of the superhero community.
Cheetah not being included in Luthor's Legion of Doom as the Superwoman counter. Some are satisfied because she still has an important role as one of the Secret Society's most powerful generals, but some think it's a missed opportunity.
Alexander Luthor being given superpowers in this new continuity, and the implication that he is now the Evil Counterpart rather than the opposite has split the fanbase yet again.
The end of issue 1 features Ultraman pushing the moon to create a solar eclipse.
While arguing with Ultraman in Issue 2, Johnny Quick gives us this gem:
Johnny Quick: So unclench that indestructible anus and get that coal-turned-diamond out of your ass!
Justice League #24 makes it painfully clear that Ultraman's parents are evil versions of Jor-El (Jor-Il in Earth-3) and Lara.
Lara: This is all your fault, Jor-Il.
Jor-Il: Just shut up and die, Lara.
Much later, we see infant Kal-Il crash land near Johnny and Martha Kent's home, here as two petty criminals and drug addicts. The first thing Kal-Il does is vaporize Johnny's hand with his heat vision and then clearly state "You two. You will be my parents now." Ultraman mentions he killed them when he was seven and razed the farm to the ground.
Issue 5 ends with the cliffhanger reveal of what destroyed the Crime Syndicate's original world: a big red crack in the sky. Readers were either unimpressed or reminded of Doctor Who.
Rewatch Bonus: Justice League of America #8 takes on new context after you read Forever Evil #3 and learn that the League's Tailor-Made Prison is in fact the Firestorm Matrix. Making the entire enterprise a Literal Metaphor for a mind prison.
The Syndicate's treatment of their hooded prisoner also takes on a new light knowing that he's a superpowered Alexander Luthor.
Unexpected Character: Nobody expected the Crime Syndicate from Earth 3 to show up. The Anti-Monitor came out of left field as well.
Special Effect Failure: One scene has a conspicuously-animated lightning bolt. Also, there's a demon baby which utterly fails to scare people. Not to mention a few cardboard photos.
Squick: The Grossest Scene In The Whole Damn Movie, where Holly appears to Marc, states that she wants to keep her baby, and pulls it out of her womb. Not even low-budget effects get in the way of the revulsion.