The whale is nicked by a harpoon, yet it is uninjured in several subsequent scenes.
In the underwater close-ups, one of the Orcas has a collapsed dorsal fin, but all shots of them on the surface show fully erect dorsal fins.
When Nolan is on the ice floe, he's wearing trousers. In the water after being ripped in, he's wearing shorts.
Whales and dolphins don't breathe automatically like humans do. They sleep with half of their brain at a time because they need to come to the surface to breathe. If someone really tranquilized an orca like Nolan did with the needle in the harpoon, both halves of its brain would be asleep at the same time, and it would stop breathing and drown.
Orcas aren't monogamous. The belief that Orcas stay with one mate for life stemmed from the fact that the same male orcas travel with the same females. It has since been discovered that male orcas stay in a family pod with their mothers, sisters, and aunts for their entire lives. Females mate with males from other pods to decrease the chances of inbreeding.
While orcas and other whales are famous for nudging objects they find curious, outright ramming them (especially at the frequency seen in the film) would still give them lethal concussions. Captive orcas, for example, have killed themselves from repeatedly ramming into their tanks.
It is constantly repeated that orcas are intelligent, and they are known to be so in real life. However, many actions of the orca in this film - starting and exploiting a peer pressure to get Nolan to fight orca, crippling the town's economy by destroying the fishing business it's dependent on, or setting a fire to a refinery - would require not merely intelligence, but a very different thing, knowledge.
Rachel, a marine biologist with a PhD who has written at least one book on cetaceans, repeatedly refers to the orca as Orca orcinus. Even a cursory look at a book on sea life will tell you it's the other way around.
Annie would have bled out from the severing of her femoral artery when the killer whale bit her leg off. However, just because emergency services retrieved her lifeless (and leg-less) body before it slid into the sea, there is no dialog to suggest she survived. Annie was the only person killed, but not eaten, in the whale's quest for vengeance. If anything, it proves the Orca had a taste for only male human flesh.
While the script keeps referring to the titular orca as a male, close-ups of its underside reveal that it's clearly female. This would actually make more sense than the alternative, as orca males are promiscuous and have nothing to do with their mates after copulation, but a sister or daughter will fight to protect an endangered pod member, and might plausibly carry a grudge.
In some of the shots of the male killer whale jumping out of the water, you can tell that it's a female killer whale because of its hook-shaped fin.
The sounds played and recorded through the hydrophone are recordings of humpback whale calls, not orca calls.
The film is set in Newfoundland, Canada. In some scenes the main character's fishing vessel flies the U.S. flag.
When Nolan yells for the ship to go hard to port, he points to his right, which would be starboard.