Continuity mistake: When Owen Shaw is shown to the team on the screen, in the first shot his last name is spelled "Shao" and in a following shot it's corrected to say "Shaw."
Other mistake: When the team get off the sub they leave the hatch open. That can only be closed manually, so the sub would have simply sunk within a few minutes of submerging.
Plot hole: Anything conducting electricity within the blast radius of the EMP, and not in a Faraday cage, would have been permanently fried. Since the whole base was within the radius (needed to take out the gate) including Dom's car and the Submarine, Cypher's plan was flawed from the beginning.
Continuity mistake: At the end of the movie in the ice chase scene, Hobbs' get away truck has tank tracks for wheels, not tires. When he rams the Russians coming from the right, you can see his getaway truck has a tire on the front left. The next time you see the truck it is back to having only tracks again.
Plot hole: Dom arrives in New York at the same time as Hobbs and his team. Dom meets up with Shaw's mum and then proceeds to steal the nuclear codes. Meanwhile at the same time, Hobbs and the team arrive at their secret hideout and start preparing the cars. The time frame isn't the same - Hobbs and co. simply haven't got the time.
Suggested correction: There are time lapses between when they arrive and the heist takes place.
Dom crosses the bridge as Hobbs and Co go underneath then Dom stops to change the spark plug a cover to have his pre arranged meeting with Shaw's mum, he then proceeds to do the heist, there is no time lapse.
Continuity mistake: The extras behind the guy Dom's cousin is indebted to keep changing in different shots.