Continuity mistake: Flash is running to power up Superman's ship. In the wide aerial shot when he dives towards the pool (after he went past Cyborg and Aquaman with their backs turned to him) notice Diana with hair in front of both shoulders. A close-up with her and Arthur follows and her left shoulder is clear of hair. (01:12:10)
Character mistake: When the military security checks Flash's phony badge, his false name "Rowe, Wesley" replaces the name of one of the names in the list to the right, one "Choi, Wesley." The problem with this is that the last names this way are not in alphabetical order anymore, so Cyborg made in fact a rather poor fake, especially for such a supposedly super-powerful being who hacked the Bat-cave computer on the fly, on top of a much larger mistake with the date of birth listed as 11/06/10, and the movie is set in 2017. (01:09:30)
Continuity mistake: After the underground battle with Steppenwolf when they are finally joined by Aquaman, Wonder Woman sums up the situation with "All he needs now is the Lost Box of Men." Batman replies "If he doesn't already have it" in another shot, where Diana's hair is missing in front of her shoulder. (01:01:15)
Suggested correction: Passage of time. You assume Batman responded that quickly and WW didn't fix her hair, as women tend to do.
I do, and I believe it is a legitimate assumption given the dynamic of the scene, rather than thinking that the hair switched place because there was am unseen, unimplied lengthy pause between her line and Batman's direct reply and that during that time she flipped a lock back without changing her stance with pendule arms between shots.
Continuity mistake: The Queen and Euboea are knocked off the horse by Steppenwolf. The Queen is face down, with the scabbard of her sword pointing up and aside of the mantle; next shot and the scabbard is not visible, just the mantle. (00:25:45)
Continuity mistake: When Barry is talking to his dad in prison, the father asks "Where do you even have the time?", and Barry is suddenly leaning with his arm to the counter instead of having that hand on his lap. (00:17:10)
Continuity mistake: Wonder Woman is on the statue on top of the Court of Justice building. She is holding the statue's sword at a different height in the two shots. (00:08:45)
Continuity mistake: The "I TRIED" sign is positioned differently against the foot of the homeless man between shots. (00:07:20)
Continuity mistake: The woman in the doorway of the Thai Street Food store reacts differently between the two shots to the dude kicking the crates in front of her; she is clutching her bag to her torso in the first shot, holding it more casually in the second. (00:06:50)
Continuity mistake: When Momoa says "He's not all right" commenting on Superman's shifty eyes when he's scanning them post-resurrection, his hair sits differently on his shoulder compared to the wider shots. (01:14:10)
Continuity mistake: Clark is thanking Bruce for the house. They both look in the distance at Lois and Martha; there are a couple guys fetching boxes near the carpenter, on both sides of the workbench, but they are nowhere to be seen in the new closer angle. (01:45:55)
Suggested correction: Passage of time. Movies don't always show every second in real time. Martha and Lois were approaching the steps, when the boxes were being fetched. In the close-up Lois is several steps up and Martha is just stepping on them as the guys with the boxes follow. It's also depth perception. The boxes aren't near the carpenter. You can see when Clark walks up. The boxes are actually several feet in front and to the right of the carpenter. It's also very possible in the close-up, they aren't in there.
I understand the caveat about the continuity in editing since they have moved away on what would amount to a couple seconds (Lois is merely on the second step), which is a hiccup some would label error in continuity already. The boxes are not right by the workbench, but still they are near as I said; let's say the person on the left who grabbed one moved to a portion of screen where he wouldn't be visible (you do see his gloved hands); the guy in red and blue should be in frame no matter what.
Audio problem: Superman uses his heat vision against Cyborg that shot at him. Cyborg deflects it and the beam destroys a patrol car in the distance, that explodes in the background without a sound. (01:14:50)
Suggested correction: There is a sound of a small explosion. Considering the distance, and we're close to the heat ray grinding on his shield, it's pretty good sound editing. We should be hearing more of the shield anyway.
Other mistake: The security guard alerts Batman about Barry Allen's arrival pushing a button on his phone. The date on the phone says it's Friday 20th Jan, which is coherent with the year (2017) this version of the movie is set in, but too early for the K-pop "As if it's your last" music video playing in Flash's lair (it was a summer release). (00:16:50)
