Deliberate mistake: Spoilers! When Black Manta is defeated, he is knocked unconscious and tumbles down a rock face after his helmet explodes on his face into the waters by the shores of Sicily. These currents and waves at best would have carried him to the rocks or the beach, leaving him on land or near it. However in the after credit scene he's somehow found out in the middle of the ocean on a broken drift wood. He would not have been carried back out to sea like that.
Suggested correction: The water is tidal. If the tide was going out, the current would take him out to sea.
There are hardly any tides in the Mediterranean Sea http://scienceline.ucsb.edu/getkey.php?key=995.
Deliberate mistake: When Walker leaves the tunnels in London and Hunt follows him, they both start their way to the Tate Modern Museum at Queens Head Passage / Paternoster Row. While Hunt is being chased and cannot choose his route, besides not knowing about Walker's destination, Walker deliberately takes a detour to Blackfriars Station and the bridge, even though he could just have walked a direct line from St. Paul's Cathedral towards Tate Modern using Millennium Bridge to directly cross to the museum and his getaway. The whole chase sequence would be obsolete. (01:31:58 - 01:36:56)