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)
Factual error: When they are trying to navigate the shuttle through Eadu, the shuttle abruptly collides with a rock, which causes Bodhi to jolt backwards. If the shuttle hitting the rock had caused the shuttle reduce speed so abruptly, in the way that was shown, then Bodhi would have jolted forwards, not backwards. (00:57:05)
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)
Other mistake: When Rogue One's team runs onto the beach after the AT-ACT follows them at the beginning of the scene it shows Stormtroopers walking next to them on the beach, but that's impossible due to the fact that all the AT-ACTs (excluding one who is moving in the water at the background) are still moving through the trees. (01:40:25)
Revealing mistake: After Jyn has retrieved the data file containing the Death Star plans, Krennic is shown walking in a hallway with two other Death Troopers and pushes a button to open a door. The door begins to open before Krennic actually pushes the button to open it. While his hand is not seen touching the button, the sound of the button being pressed is still heard. (01:51:10)
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)
Plot hole: Revelations in this film create a potential plot hole in Episode IV, in which Vader says Princess Leia is his only link to learning the location of the Rebel base. In this film, Vader captures the Profundity (Raddus' command ship), which is transporting the Tantive IV in its cargo hold. Vader then watches the Tantive IV fly away with the Death Star plans, leading into the beginning of A New Hope in which he captures that ship. So, the first question is, were there no survivors of the Profundity Vader could interrogate to learn of the location of the Rebel base (assuming the navicomputer has been scrubbed). Even if the entire crew were killed, in A New Hope we see several crewmembers of the Tantive IV have been captured. This film shows that the Tantive IV was at Yavin prior to the battle (evidenced by R2-D2 and C-3PO in the hangar). That then raises the question of why Vader couldn't have interrogated those other crewmembers to learn the location of Yavin as the Rebel base.
