It would have been cool to hear them talk about Skyhook a bit, but I’m content with what I saw.
Vader thinks the plans are in the computer having (presumably) not found them on the Profundity, but they’re actually physical copies, which he doesn’t know, and everyone is there “to stop [him] this time.”
The Rebel troopers stall Vader to give the others time to get the plans off the Profundity’s computer and onto the Tantive IV. Vader realizes the plans aren’t there and are probably on the fleeing corvette. He chases it down.
Captain Antilles stalls Vader to give Leia time to get the plans to Artoo. Vader learns the plans aren’t on the computer and that Antilles was stalling (and actually doesn’t know anything), so he kills him and orders the troopers to find the passengers who might have the plans. They find Leia, who’s just given them to Artoo and causes a distracting ruckus.
Leia stalls Vader to give the droids time to get to the planet. The Star Destroyer gunners don’t know what’s going on with the boarding party and the plans, so they ignore the “malfunctioning” empty escape pod, allowing the droids to escape. Meanwhile, Vader knows Leia is lying, but also knows she knows something about the Rebels (she shot obviously-Imperial troopers on a ship that just fled Scarif) so he captures her, hoping to learn about the Rebel base. As control of the Tantive IV is consolidated, Vader is told of the escape pod and realizes she might have hidden the plans there before jettisoning it, orders the commander to send a detachment of troopers down to get them, and says “there will be no one to stop us this time” because he’d just been frustratingly stalled over and over, not realizing she gave them to a couple of droids who will give the afore-mentioned detachment the slip, and then again when they escape a locked-down Mos Eisley, which ultimately leads to the destruction of the Death Star.
The thing about the Death Star plans is that, while they mean everything to the Rebellion, because (we now know) they know about a hidden flaw in the construction of the station… most of the Empire doesn’t seem to care so much, partially because they don’t know what the Rebels do. Vader isn’t interested in the station compared to the Force, especially after he realizes Obi-Wan is still alive. Tarkin and most of the officers (except Motti) think that the station is invulnerable no matter what the Rebels know about it (again, the Empire doesn’t know about Galen’s “fuse” until Captain Bast tells Tarkin that they’ve analyzed the Rebel plan of attack, Krennic was the only Imperial who truly knew about it). Vader and Tarkin even let our heroes go (remember, they know that the the ship they captured in the remains of Leia’s home planet blasted out of Mos Eisley which is on the planet where they lost the plans, not to mention that Obi-Wan Kenobi came out of retirement for this, they know they let the plans go to the Rebels) in order to lead them to the Rebel base, which is their true main objective.
The last minutes of Rogue One and the first act of A New Hope is basically a lot of luck (or the Force =P) and stalling the unstoppable forces that are Vader and the Empire just long enough to keep the plans one step ahead of them.
This all feeds into Vader being more of a lackey character in Episode IV, too. He kinda fails his way through Star Wars, really. He fails to get the plans, he fails to destroy the Rebel base, he gambles with the Death Star and loses it. Vader doesn’t come into his own until he discovers Luke and becomes very driven to find him.
To me, it’s amazing that they were able to weave a new story in so closely to such a revered and sacred (to us) story with very minimal shoehorning or toe-stepping.
