Plus the plans only got to the rebellion after Vader personally failed to stop a piece of physical media from escaping the airlock where he was slaughtering rebels. This happened despite him having telekinetic powers, because he chose to use them on rebel soldiers and not the obviously valuable item they were clearly trying to smuggle out at the cost of their own lives.

And it just so happens that the ship those plans got onto was his daughter's ship. And when he "captured" her, she just happened to choose his old astromech droid and the protocol droid that he built as a kid to carry the plans off. And those droids got out in an escape pod that just slipped past a fully armed star destroyer because obviously there couldn't be anything valuable slipping past that might warrant firing up one of their many lasers or tractor beams.

And the planet they were over? Tatooine, the ass end of nowhere, a wasteland ruled by the Hutts which has no rebel presence whatsoever, but which just happens to be Vader's home planet. And those droids, who could have landed anywhere on that entire planet, by sheer coincidence, land right by the farm where Vader's step brother is looking after his son. And those droids take the son and the plans to Vader's best friend and teacher, who has not been part of the rebel alliance, and couldn't possibly know of a secure place to pass them along.

From there, a disgraced former imperial officer with a lot of debts to pay agrees to take the group to the planet that happens to be where the death star is waiting. This happens only after the former imperial carries out the murder of a childhood associate of Vader. And they only manage to escape because the troopers who have them outnumbered and outgunned yell a warning and fire wildly, completely negating the element of surprise.

And don't even get me started on the death star escape or the battle of Yavin. There's just too much. How does a moon-sized planet-killing space station not have enough fighters to overwhelm a dozen x-wings and y-wings? How does a transport get the drop on an ace fighter pilot with functioning sensors, wing men, an entire goddamn space station backing him up, and oh yeah, FREAKING PSYCHIC POWERS?!

By the way, that transport? Previously registered to the man who handed control of Bespin to Vader. But I'm sure that's just a coincidence. I mean, it's not like he blew up a death star or anything..... oh wait!