Other mistake: After realising they can track the mother box, Batman says they have to go back to his base to use one of his satellites to track it, and they all do so. Which completely ignores the fact that Cyborg could easily access the satellite feed directly using his abilities and display it to the others on any nearby screen in Star Labs.
Other mistake: Barry comes back to his home, replaces the fuse in the fuse box, flips the handle (begs the question of why remove the fuse AND turn off the switch, but whatever), and within 2 seconds every screen in the place is lit up. Sure, a TV might come on that fast, but plenty of those screens are showing data, analysis, etc, running off computers, which would take longer than that to boot up and get everything running.
Plot hole: WW mentions that "As Darkseid waged war on Earth, he found a secret there", that being the Anti-life equation. But later on it turns out that after being defeated, planet Earth is so "anonymous among a trillion worlds" that he never manages to find it again and destroys another 100,000 worlds (his words!) to look for it again. That would mean that they lack any sort of navigation, and it's hardly possible anyway that the planet would be "anonymous" when it contains what Darkseid wants the most.
Factual error: In Part Two, as Diana explains to Bruce Wayne the history of the Mother Boxes on Earth, we see an extended flashback of Earthly gods and warriors in epic battle against Darkseid. When Diana says, "A golden age of heroes fighting together," we see a closeup of an Amazon archer drawing back an arrow right-handed, leaning right, and releasing it. However, the arrow is UNSUPPORTED on the bow, so she couldn't possibly aim or control the arrow. A truly amateur mistake. (01:03:59)
Other mistake: Apparently, one of Aquaman's superpowers must be to be super-heavy, since surfing on the body of a parademon he lands on a five story building and that somehow slices the whole building in half, complete with explosions that leave him unscathed and don't turn the parademon's carcass into a pulp. (03:15:15)
Revealing mistake: After Wonder Woman kills the final terrorist with a huge blast, debris rains down on the police below. Not only are none of the officers injured, the debris doesn't cause any damage to the vehicles whatsoever. There are no broken windows, broken windshields, broken light bars, or any dents and scratches despite massive chunks of the building falling all over the vehicles.
Revealing mistake: One of the amazons (apparently called Epione) is standing to the right of the chamber doorway and shoots arrows protecting the queen. When Hippolyta runs towards the wall to do a fancy move after fetching the Mother box, you can see Epione being tossed to the wall by the parademon bolt a moment before the CGI bolt reaches her. (00:29:15)
Revealing mistake: When the military security checks Flash's phony badge, the name on the personnel list to the right does not match the fake identity; Barry's false identity is "Rowe, Wesley", but in the list the name "Band, Ryan" is highlighted. This mistake was not present in the theatrical 'Whedon' cut where the name was altered to match. (02:27:05)
Other mistake: Before Wonder Woman bursts into the room with the terrorists there's a cut to the schoolgirls watching the bomb about to blow. The girl to the far left is actually cracking a laugh. You may justify it as a hysterical reaction (she does the same in the foreground when the baddie turns the key), but appearing just in brief moments and with her looking properly afraid in other shots, it just looks wrong. Whedon's version didn't feature the corpsing. (00:20:40 - 00:21:35)
Plot hole: The heroes find Steppenwolf's base thanks to Cyborg's dad, who superheated the core of a Mother Box so it shows up on a thermal scanner. But the box itself wasn't emitting any heat on the outside, and a satellite can't magically infer the internal heat of an object if it's not conveyed to the surface. If Wayne has such precise satellite sensors, it would also spot a nuclear plant suddenly drained from radiation, and the intense energy (and heat) caused by Steppenwolf's activities.
Other mistake: In this version, Queen Hippolyta whispers "Return to me, Diana" as she shoots the arrow, as opposed to "Listen to me, Diana" in Whedon's version. Whedon's line made sense, since it was a warning, this does not, since Diana never comes back to Themyscira nor she is supposed to, being busy thwarting the invasion in the Land of Men. There's no reason why the Queen would say that line. (00:43:10)