I think they did intercept something. In episode IV don't they tell Tarkin they've analyzed the attack and found a small danger? That means they may have figured out about the weakness during the battle of Yavin, or earlier. They just thought the odds were to great for an attack to be successful.
Another thing - we're supposed to believe the information could be beamed up to those ships but they couldn't beam it all over the galaxy from their ship and the plans could only be taken (inside R2D2) in person to Obi Wan. Kinda silly. I guess that's why they had that HUGE satellite - to make it seem like that was a requirement for sending information in this world (aside from holograms).
Yeah, that whole part was pretty contrived. As far as getting it to Obi Wan, they apparently didn't know where he was exactly let alone him have the ability to receive the transmission so I wouldn't quibble with that. But they had voice communication through the shield but not data? Don't think so. And they could also communicate with ships traveling at light speed so they had to have some sort of "sub-space" (to use a Star Trek term) communication as well.
Maybe the Rebel fleet didn't transmit the plans to the rest of the galaxy so as not to let on what the flaw was to the Empire so they couldn't correct it. This might be the case if the only place Galen Erso documented the flaw was in the schematics kept at Eadu. Presumably any schematics kept on the Death Star itself wouldn't let on what the flaw was. OTOH, it seems like the Death Star would have intercepted the initial transmission, so it's still a plot hole. :
I guess the Rebels knew that Galen Erso had designed a flaw in the Death Star, so they were looking for the flaw. But the Empire just thought the Rebels wanted the plans to figure out how best to attack it. So the Empire wasn't looking for, and maybe didn't fully appreciate, the weakness designed into the Death Star. But it still seems like an incongruity in the plot, as Moiraine pointed out.