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)
Other mistake: Director Krennic is shorter than Tarkin in their scene together. Krennic comes up to Tarkin's ears at best. Krennic is also shown to be about the same amount shorter than Darth Vader, roughly coming up to Vader's ears as well. But as shown in A New Hope, Tarkin is considerably shorter than Darth Vader. So by what was shown in A New Hope, Krennic should be much shorter, perhaps coming up to Vader's chest.
Answer: Princess Leia is not being chased by Vader's ship until after the events of this movie. The entire fleet heads off to Scarif, and she picks up C3PO and R2 off-camera. At the battle on Scarif, we see the mothership get boarded by Darth Vader, and then we see the smaller ship make their escape. That ship contains Princess Leia and the two droids, which is subsequently being chased at the beginning of Episode IV.
jshy7979