Continuity mistake: The extras behind the guy Dom's cousin is indebted to keep changing in different shots.
Continuity mistake: When Dom is taking the panels off the car at the start, his cousin goes to take a sip of coke. Camera changes and his hand is down by his side. (00:05:00)
Continuity mistake: When Cypher is explaining what brought her to Cuba, she is looking at Dom. Camera changes and now she is facing away from Dom. (00:13:20)
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: 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: Near the end, the Russian chase vehicle fires a grenade at Hobbs' vehicle. The tube on the top far right is used and can be seen open. When that same vehicle goes for the second shot at Hobbs, the tube that was used before is unused now. When Dom hits the vehicle shortly after that there is a very close shot that shows that despite having just fired another round the array of tubes is again unused. (01:51:05 - 01:51:55)