Other mistake: Max broadcasts his speech in English, but everyone in the world understands him just fine. The movie never established that Max can be understood by anyone at the same time, and we hear the broadcast in English (if the movie wanted to convey that to other people he sounds in his own language, they would have showed that). (02:02:40)
Audio problem: When Diana walks away from Steve, he yells a final line that is noticeably dubbed over - does not even sound like Chris Pine's voice. (01:58:05)
Revealing mistake: Steve Trevor approaches and stands before an oval, wall-mounted mirror, incredulously looking at himself and seeing a stranger's face in close-up. Steve finally smiles approvingly, turns to Diana Prince and says, "He's got it! Y'know, I like him!" The camera immediately cuts to two wide shots from behind Steve standing directly in front of the mirror (only a couple of feet away from it), but there is no reflection of Steve in the mirror at all. This error reveals that the "mirror" is actually a hole in the wall (a low-budget practical effect used in films of decades past for such mirror illusions). They probably filmed a lot more footage of Steve mugging in front of the "mirror" but edited it out, because this old-school effect is notoriously difficult to get exactly right. (00:49:50 - 00:50:20)
Suggested correction: They don't use this trick for the scene, the actor playing "the other guy" is standing in front of the mirror himself when you see him in the reflection, since he has black hair and Chris Pine does not. And Chris Pine can only be seen without the mirror. Later in the wide shots the angle of the mirror simply doesn't show Chris Pine's reflection. Only a tiny second at the start of the wide shot can you see it is actually a real mirror, when you see a piece of Chris Pine's hair in it.
As I said, they probably filmed a lot more footage of Steve mugging in front of the "mirror" but edited it out. When Steve approaches the "mirror" in close-up, you can see that there are two distinct actors (which is the whole purpose of the scene): Chris Pine's hair is a distinctly different color and texture, and the actor in the "reflection" is taller. Plus, their subtle body and head movements are not perfectly synchronized, as would be the case in a true mirror-image. It's the old hole-in-the-wall trick.
But it is a real mirror, as it reflects his hair. So it's not a hole in the wall anyway. The back of the head you see when seeing "the other guy" in the mirror is that same guy's head, not Chris Pine's. No need to use that trick.
No, the hair color and texture of the back-of-the-head shot are distinctly different from the guy in the reflection. The whole purpose of the shot is that Chris Pine in the foreground IS NOT the guy in the reflection in the background. The hair color and texture is different, and the guy in the reflection is taller; plus, the body and head movements are not synchronized. Go back and watch the scene (if you can stand watching the movie again).
Revealing mistake: When Cheetah is under fire from the security of the White House and runs towards the camera to grab a column and swing around it like a pole, she is not Kristen Wiig - appears to be a purely CGI shot. (01:50:25)
Revealing mistake: When Barbara is checking out the microfilms that talk about the mysterious stone, you can see in the last one just before the close-up on her eyes that it bears the date "1986", posterior to the movie setting (you may need to pause to read the full paragraph, which says indeed "During 1986, sections were drawn", and it's also worth adding that you can also spot easily that most paragraphs are recycled from one slideshow to the next). (01:13:40)
Continuity mistake: After Diana refuses his wish, her wounds understandably heal themselves as her powers return, but the blood on her shoulder and chest also disappears.
Visible crew/equipment: When Wonder Woman's going under the truck during the desert chase, look closely and you can see the mechanic's creeper the actress is lying on.
Continuity mistake: When Max calls himself "a pretty messed up loser-guy", his hand is on his son's chest, then under the armpit at the cut. (02:21:20)
Continuity mistake: Wonder Woman loses the grip on her lasso of truth when she Tarzans her way towards the kids, but the moment she turtles up in front of the incoming escort vehicles the lasso is there on her belt. (01:25:40)
Continuity mistake: After the battle feat when she pushed a truck for hundreds of meters at cruise speed shielding herself from bullets, Wonder Woman hides with her back to another truck bed. Gal Gadot's hair is across her face, or not, depending on the shot. (01:22:40)
Continuity mistake: Barbara kicks the Dangerous Drunk one last time, and we see him fall with the feet next to the curb of the sidewalk. The man is still conscious and tries to move, seemingly to crawl forward, but we do not see him even budge, and when Leon the cultured hobo arrives mere seconds later the guy is unconscious and can't even move, but he's in the middle of the road now. (01:16:05)
Continuity mistake: Diana asks what could be imbued into the stone; Steve is trying to guess and goes "I don't know, hmm." The ring with the Gods' writing is in a different spot of the table compared to other shots (for instance, there's a page in between the jewelry and the other pointed dark item on the desk, absent in other shots). (01:05:40)
Continuity mistake: Diana is looking at Steve's amazed face reacting to the subway train. In the wide shot she has her hands on her hips initially, but before the cut she brings the arms fully down her sides. However, in the next shot she is again looking at him in the initial pose. (00:58:05)
Continuity mistake: Steve gets a leaflet from the astronaut and approaches the stairs by the Jupiter-C model. When he coos in the next shot on top of the stairs, the people on the floor changed from the previous. (00:59:10)
Continuity mistake: Throughout the whole scene where she first interacts with Diana, Barbara's briefcase changes orientation in the closer shots on Kristen Wiig. For instance when she gets all giddy about the FBI involvement and asks "They're coming here?" the clasp on the suitcase is to the left (towards her hands), but then she replies "My help?" and the metal parts are exactly in the opposite direction. (00:21:00)
Continuity mistake: The criminal is holding the kid hostage dangling her outside the platform. His partners in crime try to talk him down; the curly haired guy with the sage jacket is waving with one arm, then the other; the bag switches hands. (00:14:40)
Continuity mistake: Max's secretary tells him that the Wall Street Journal wants to interview him; she holds the phone with the right hand on the microphone and the left hand above it, but she's waving the phone in her right in the next shot, the left hand being on the cable, several centimeters below. (01:00:40)
Continuity mistake: When Diana picks up the receipt at the bottom of the artefact's box, the slip changes position between her hands between shots, and she is holding it with just the left hand in close-up, with both in the wider angle. (00:40:00)
Continuity mistake: During the riots, Diana and Steve say goodbye to each other. She holds his face (imaginary one as it is) between her palms; he mentions "This crazy new world" and Gal Gadot's thumbs are on his cheeks, but immediately behind his ears in the reverse shot. (01:57:10)
Continuity mistake: Once Barbara frees Maxwell from the handcuffs, she looks at him and says "Go." By Wonder Woman and the chair in the background there's a woman holding some papers, and she was not in the action phase before. (01:52:10)