Corrected entry: It is stated that the USS Franklin is the first starship to achieve warp 4, despite being commissioned after the Federation was formed. Enterprise NX-01 in the series Enterprise achieved speeds in excess of warp 5 long before this, which predates the Kelvin timeline change.
Corrected entry: When the Franklin is in freefall from the cliff, all of the bridge crew are leaning forward, but they should be being pushed back into their seats.
Corrected entry: When Jay-lah and Scotty go to check her trap, Scotty picks up a large stone. You can tell it's a prop as there is no weight to it when he picks it up.