New this month Continuity mistake: The surveillance video of Hawkgirl talking to the Justice League is different than what we saw in the previous episode. She doesn't move towards Bruce in the video, people are in different positions, and Clark has glasses on in the video.
Continuity mistake: When Flash plays tag with Faust ("Now you see me, now you don't"), there is a brief shot in which he rushes at Faust - but not inside Hyppolita's palace, but in some high-tech laboratory. Obviously a shot from some earlier series, since the coloring and style are different from the Justice League's.
Other mistake: When Lex finally manages to open Batman's utility belt and spills out its contents, we see several hand grenades dropping out of the pouches. However, these grenades are standard military egg grenades, and with their size and bulk they should have bulged out the square pouches in which they had been kept - if they had ever fitted inside in the first place.