The opening scene of the movie is set in 1975, but Warren Zevon's "Werewolves of London" is heard on the radio, which wasn't released until 1978. However, due to the time traveling events that Wolverine did in Days of Future Past which altered the time line.It caused a ripple effect in which Warren Zevon would've recorded the song earlier, possibly from seeing Beast in his blue form that was recorded in Paris might also have contributed to it as well.
When Jean is reading Charles' mind in New York, in the flashback, Charles can be seen driving an eight-year-old Jean to the school, but it was established that he was in a wheelchair then and had no control over his legs, and therefore couldn't drive. But Days of Future Past revealed that he sometimes uses a drug to regain control of his legs (at the temporary expense of his powers), so it's possible he took minimal enough of a dose to be able to drive the car.
If the D'Bari were so powerful that they can absorb the Phoenix Force, why didn't they do it in the first place when the Phoenix Force was destroying their home planet? Vuk, the leader of the D'Bari, mentioned that the Phoenix Force destroyed everything it came into contact with until it merged with Jean. Jean had to willingly transfer the Phoenix Force to Vuk in the first place, so it stands to reason that the D'Bari can't forcefully take it from her.
Mystique, Cyclops, Beast, Storm, Jean, Quicksilver, and Nightcrawler mutant abilities do not allow them to survive space. The X-men save astronauts whom are wearing protective suits while wearing leather jackets.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
Mystique is killed in this film despite being alive & well in the original trilogy which is set after the events in this film. This is a film set in an alternate timeline from the original X-Men trilogy, not a prequel to it, so this is not an error, nor is anything else that contradicts events from those films. Furthermore, the ending of Days of Future Past "undid" the events of those movies altogether.