Continuity mistake: It was briefly stated in the second film that the T-Virus was created by Dr. Ashford to cure his daughter Angela and that the Red and White Queens were based on her. This movie contradicts that by suggesting that Dr. Marcus created the T-Virus to cure his daughter Alicia, and that the Red/White Queens were modeled after her. While the rest of the movie stays true to the continuity of the previous films, this rather obvious ret-con is still a major continuity gaff.
Plot hole: At the beginning the Red Queen said that the last human settlement will fall in 48 hours unless Alice releases the anti-virus, however when Alice does release the anti-virus (a few seconds before the timer ends) she says it will take years for it to reach around all the corners of the globe, this does not make sense and implies that the last human settlement will fall anyway.
Other mistake: Alice is running behind the armored cars. Once she manages to get on top of the car, suddenly the zombies that were only behind her and nowhere near the car are found at the sides too, attacking a guard and later Alice as well. Not possible considering if zombies were able to get there, they would have killed Alice while she was running.
Continuity mistake: There is a scene of Alice being dragged by a line behind Isaacs' tank ahead of a horde of zombies. There is no other line next to running Alice. When she climbs upon the tank to attack the guard, another line with torn hands is seen being dragged on the road, where Alice was dragged. (00:21:15 - 00:23:45)
Plot hole: At the end of Apocalypse the Umbrella corporation bombs raccoon City. It doesn't make any sense that they would do this with the entire Umbrella high command underneath the city, as we learn it is in this movie.