The goof item below may give away important plot points.
The future Enterprise is a Constitution-class vessel, registry number NCC-1701. Admiral Kirk and Ambassador Spock are on-board. Spock says that they are from the year 2373. In 2373 Kirk would be 140 years old, and Spock 143. Also in 2373 the Enterprise is a Sovereign-class vessel, registry number NCC-1701-E.
According to the Star Trek movie (2009), James T Kirk was born in the year 2233. Admiral Kirk and Ambassador Spock go back in time to assist. Spock states that they are from the year 2373, which would make him 140 years old.