Broken Base: Although fans are ecstatic that the original voice cast returns for the Justice League, many felt disappointed that the Legion of Doom was altered. Either the Legion isn't as great because many of the original members are absent or it's better because we see other unappreciated characters shine in the spotlight.
Complete Monster: Vandal Savage is a conqueror with genocidal plans for the planet. He manages to steal the protocols that Batman designed to defeat the Justice League in case one or more members of the Justice League turn evil. Savage makes these protocols more lethal and sadistic and then uses them to take out the Justice League. After his Legion of Doom seemingly triumphs over the Justice League, Vandal Savage informs them he plans to conquer the world by using a missile that will cause a solar flare that will kill half the world's population. This event will also render the rest of the world's population so weak and helpless that they will naturally accept his leadership.
Crack Ship: Some fans ship Batman with Cheetah, for some reason. However, the two never actually interact at all together and are never even in the same frame. This is most likely heavily influenced by a scene from the Justice League cartoon where Batman seduces Cheetah while being held captive by Lex Luthor's Injustice Gang.
There's a brief scene where we see Cheetah describe Wonder Woman as "so hot". It's not actually Cheetah saying this, just a civilian who looks and sounds like Cheetah because Wonder Woman is hallucinating. But the subtext is there regardless, and there's nothing to suggest the civilian was a guy...
Ma'alefa'ak attracts Martian Manhunter's attention by taking the form of a seductive blonde woman and buying him a drink. He acts no less seductive even after J'onn finds out who he is. Did we mention they're brothers? (even if the movie itself didn't)
Genius Bonus: When J'onn is told that poison he drank is largely magnesium which will sweat out through his skin, it creates a special Oh Crap! for the audience who knows that that metal is special in that it's flammable. Magnesium flames also can't extinguished by water. Magnesium burns with a white flame!
It Was His Sled: Anyone who's read Tower of Babel will know that the movie ends with Batman quitting the League.
Squick: Again, Ma'alefa'ak attracting Martian Manhunter's attention by taking the form of a seductive blonde woman acting no less seductively even after J'onn finds out who he is, when you take in account they're brothers in the comics.
Batman's contingency plans may seem extreme, but how can you have a group of basically Physical Gods and not have a way to keep them from becoming a danger to humanity? We also have to take into account the fact that Batman makes it clear that his plans were to disable the League, not kill them. He then explains that Savage took the basic plans and made lethal versions of them. This is in contrast to the comic, where Batman's plans were much more fatal and made that way by design, meant to be implemented if Bruce was ever going against a Justice League member in a me-or-him style fight.
One of the producers narrating a making of documentary on the feature remarked that Batman had the right idea but his execution was wrong. The main argument for Batman's contingency plan is the question of competence. Not only should it have been impossible for a supervillain to learn of the existence of these contingencies but the easiness with which his security gets breached pretty much renders his reasoning moot.
It's also important to remember all the times the League's members (both individually and as a group) have had their powers stolen, been cloned, succumbed to mind control, etc. Pretty much every single one of them has had all of these things happen at one time or another.
Some fans have expressed unhappiness at the decisions to replace Aquaman with Cyborg, Kyle Rayner with Hal Jordan, Ra's al Ghul (The Big Bad of Tower Of Babel) with Vandal Savage and the Legion of Doom, and the omission of Plastic Man. The fact that, despite Michael Rosenbaum voicing the Flash, that it's Barry Allen and not Wally West (whom Rosenbaum voiced before) has also taken some people aback. Some fans who were introduced to the Green Lantern through the animated Justice League also were left with the short end of the stick with what could feel like a random replacement of Hal Jordan for John Stewart, despite Stewart not appearing in "Tower of Babel".
Also the name was changed from Tower of Babel to Justice League: Doom, however, this was a edit that was changed by TMS to avoid legal issues with Namco Bandai (link of the game here).
Lois Lane sports a starkly different model than other productions or comics, for some reason having Wonder Woman's distinctly Greek features, which has met with confusion and occasionally scorn from fans.
A lot of fans also hate the changes made to Batman's failsafes, in particular the Green Lantern and Flash traps (which were appropriately the most radically changed of the lot).
Unintentionally Unsympathetic: Batman. While we're probably meant to sympathize with Batman's stance on having contingency plans to take down heroes who are practically gods among men, he's such a nasty jerk about it that it's hard to side with him (even after he gets buried alive with his dad's corpse).