According to the timelines shown on screen, the story starts in 1960 and ends in 1961. However, in one of the scenes on the ship, in the background you can hear JFK's speech about the Cuban Missile Crisis from October 1962.
In the scene where the Albatross comes across the Cuban Military Patrol Ship, electronics on the Cuban ship, most notably the Radar System, weren't available in the configuration seen in the early 1960s.
At the beginning of the film their is an establishing shot of Charles Gieg's (Scott Wolf) house which we are told is in Connecticut. The trees are full of Spanish moss which typically is not found north of Virginia and has never been found north of Delaware.
During the sinking of the schooner the radio in the background is describing the final moments before the launching of Freedom 7, the spacecraft carrying Shepard - on May 5, 1961. However, the schooner sank three days previously on May 2, 1961, and the survivors were rescued on May 3.
In the scene when the boys are discussing the hearing Etham Embry's character says the ship went over because she was gybed. The term 'gybe' would never have been used on the 'Albatross' as you only gybe dinghies or yachts. On a square-rigger you would wear ship.
When the Cubans have boarded the Albatross, they threaten to take Lapchick with them because he does not have his passport. As this is happening, Dean yells "if he's Cuban, Castro wears a dress", which doesn't match what he's actually mouthing. The scene was obviously dubbed, possibly for the MPAA or the director simply liked the other line better.