In the opening scene, when Gorr is in the garden, notice that Christian Bale's eye mole switches sides - some shots were obviously flipped.
(at around 1h 10 mins) In Thor: Ragnarok (2017), Korg says that he has a mother. In this movie, however, Korg says that two dads are required for Kronan reproduction.
(at around 58 mins) When Thor get stripped naked by Zeus, Zeus' whole crew (for the lack of a better word) faints at the sight of Thor's crazy hotness. In the very next scene, they're all back up on their feet, same position as before they fainted, just as if nothing happened.
During the time Zeus was addressing Thor, his Thunderbolt was first on the mount behind him, then off, then on again, without ever being taken off.
(at around 16 mins) When Jane is in hospital with Darcy early on in the film, the snacks Darcy has on her table change places during back and forth shots.
(at around 33 mins) During flashbacks, Thor displays an incoming call on his cellphone from Nick Fury, but the last name is spelled "Furry." This is a joke revealing that Thor doesn't know how to spell Nick Fury's name correctly.
When the flying boat crashes into Gorr's planet. the name on the boat is backwards, revealing the use of a mirror image.
(at around 33 mins) In Thor: Ragnarok (2017), Doctor Strange said that he wasn't able to contact Thor because Thor didn't have a phone. However, in the flashback scenes in this movie (which take place prior to Ragnarok), Thor is clearly shown to be regularly using a personal phone to receive mission updates from Nick Fury. In addition, since Thor uses a smart phone in these scenes, it makes less sense for him to have not been aware as to how emails are sent in that same conversation with Doctor Strange.
(at around 1h 24 mins) Stormbreaker is shown to have a consciousness, displaying an attitude towards Thor and disobeying his commands at times. Yet when Gorr captures Stormbreaker, the ax makes no effort to resist his will, behaving as an unthinking, unfeeling tool.
(at around 1h 24 mins) If the axe and hammer can be called from anywhere then why didn't Thor can just call his axe back when Gorr takes it from him.
When Sif is waiting to die from her injuries after battle so she could go go Valhalla, Thor tells her that she has to die in battle in order to go to Valhalla. However, at the end of the movie, Jane goes to Valhalla when she dies after battle.