Other mistake: They show the tether and tether anchor fall out of the ship and fall behind, much in the same way as throwing something out of a car. However, it was still in the warp bubble and should have continued to be moving at warp 5 with the ships. We see later Columbia extend its warp bubble around Enterprise and Enterprise remains at warp 5 after cutting their engines. But, if the tether is no longer affected by the warp bubble, it should have been instantaneously out of view.Bishop73
Trivia: A film reference to Star Trek: First Contact: Archer says something about a group of cybernetic creatures (The Borg), that tried to stop Cochrane from launching his mission into space that was stopped by a group of humanoids, that were also from the future (USS Enterprise NCC 1701-E).