Continuity mistake: When Krennic is first talking with Galen Erso on his home planet, the coat that Galen is wearing is visibly drenched, presumably from rain water, but later in the scene, when Lyra Erso intervenes, the dampness on his coat is now much lighter. (00:03:30 - 00:05:10)
Suggested correction: We know from Episode IV that some fabrics in the Star Wars canon dry very quickly, see the garbage compactor aftermath. This is totally possible.
I'm not sure if this is a viable explanation. While some aspects of life in the Star Wars universe are somewhat fantastical (the ways of the Jedi for example), this universe still follows the same basic psychics of Earth, so for example, something like gravity or the speed at which something dries would still be the same. (As for your Episode IV reference, I'm not sure if that counts as a defence, or is just a mistake in of itself).
Continuity mistake: When Galen and Krennic are talking at the farm, in some shots the wind is very strong, judging by Krennic's cape and Galen's hair. In others there's virtually no wind at all. This changes immediately between shots, there's no time for the wind to swell or fade. (00:03:30)
Continuity mistake: At the start when Andoor meets Tivik, Tivik's coat over his shoulders keeps moving between shots - on both shoulders, then on one, then both, etc. (00:10:05)
Continuity mistake: When Bodhi Rook is first introduced on Jedha, there is a fallen statue in the sand, first shown lying on its left, but at the end of the scene, the statue is suddenly lying on its right. (00:11:15 - 00:12:15)
Continuity mistake: When Director Krennic and Governor Tarkin are discussing testing the Death Star, Krennic says he will not fail and turns around to leave. As he turns, an Imperial officer is seen standing a couple of meters away from him in the background, but in the next shot, the Imperial officer is suddenly right behind him. (00:23:20)
Suggested correction: That is not correct, Captain Dunstig Pterro is not that far, and Krennic moves pass him and then Pterro follows.
Continuity mistake: At the point of the movie where K-2SO slaps Cassian on Jedha, you can see Cassian cover up with his face to cover his smile, as the entire slap was improvised, then a shot with his hand down, and then back to a similar shot of the first one with his hand covering his face. (00:34:20)
Continuity mistake: When Baze shoots all the Stormtroopers, he begins walking over to Chirrut. Chirrut is seen placing two hands on the top of his staff, and then puts one hand lower down on the staff, holding it with just that hand. In the next shot, he is suddenly holding the staff with both hands. (00:35:55)
Continuity mistake: When Baze points his blaster at K-2SO, Jyn tells him that he is with them. The shot cuts back to Baze and Chirrut, with Chirrut saying "They're all right" and Baze still has his blaster pointing forwards. In the next shot, Baze's blaster is suddenly lowered slightly. The shot then cuts to Jyn and K-2SO and when the shot cuts back to Baze and Chirrut, Baze is now seen lowering his blaster that is now suddenly raised again. (00:36:05)
Continuity mistake: When Jyn meets Saw, in most shots the hose for his mask is well through the loop on his suit, but in one closeup shot the mask is right up against the hose, then jumps back. (00:40:00)
Continuity mistake: After the facility on Eadu is ambushed by the Rebellion, Krennic is escorted back to his ship and looks back at Galen Erso's body. When he looks over, Galen is shown with his right leg completely straight and his left leg at an angle, but when he is next seen, a few shots later, it is now his left leg completely straight and his right leg at an angle. (01:07:35)
Continuity mistake: When Jyn reunites with her father after the attack on Eadu there are a few strands of hair draped in front of her, with some on the left side of her forehead and some on the right, but a few shots later, the strands of hair are now draped evenly. (01:08:05)
Continuity mistake: As the shuttle lands on Scarif, the man doing the ground guiding kneels in the dust and thruster wash. From another angle, the man has suddenly disappeared. (01:27:45)
Continuity mistake: When the Rebel fleet arrive at Scarif, they arrive close to the shield gate and the Imperial fleet. However, when Blue Squadron makes their attack run, they are suddenly high above the shield gate. (01:38:05 - 01:38:40)
Continuity mistake: When the Death Star fires on Scarif, Jyn and Cassian settle down on the beach and Jyn is shown with her back straight whilst she is kneeling, but in the next shot, she is suddenly leaning more forwards. (02:02:25)
Continuity mistake: When Jyn and Cassian are hugging on the beach after the Death Star has fired on Scarif, the first shot from behind Jyn shows her hugging Cassian with one arm, but when the shot cuts to behind Cassian, she is suddenly hugging him with both arms. (02:03:00)
Continuity mistake: When Vader appears at the end, the amount of rebel soldiers facing him changes throughout the scene from about 8-12 as Vader makes his way through them.
Continuity mistake: When K is at the control panel he shoots two stormtroopers to his right. He then says stardust and moves his aim slightly to his left and shoots the same two stormtroopers again - the first two stormtroopers have disappeared from the floor.
