The film required you to accept too many leaps of faith. Blake knows Bruce is Batman because of a look on his face when he was a kid? Knowing...."Hey I lost my parents...so did this guy.....but look at him faking his way through the pain....he must be Batman."
This was the main one that I felt was a bit too much. He should have had some reason for knowing that Bruce Wayne was Batman. It is pretty easy to figure it out (billionaire who's been hurt by crime returns to Gotham, and shortly afterwards a vigilante with incredibly expensive equipment and a lot of free time is running around), but we're kind of forced to assume it's a lot more difficult to figure it out in universe than it would be for us (or else everyone in Gotham would have guessed it by now). So having a character just figure it out like that makes everyone else in Gotham seem like idiots.
As for how he got back, I don't see why so many people think it's a plothole. Wasn't it 23 days or something like that since he got out of prison until he returned to Gotham? More than enough time for him to get back to America. As for getting into Gotham, I doubt there would be many individual civilians trying to sneak
in to the city - security from both Bane's people and the army would be more focused on keeping people from leaving. Also, he is supposed to be well trained and very skillful - we accept him performing incredible feats of stealth off screen all the time as Batman, such as when he suddenly appears behind villains or just disappears. It's pretty easy to accept that he managed to sneak past some guards - they probably just decided that that wouldn't be such a great scene so decided to leave it out.
Some other things that are more like plotholes (or just seem a bit stupid) are things like how he knew exactly what day the bomb was due to go off when he had been away in prison, and how he must have spent a considerable amount of time painting a giant bat symbol in fuel (How are so many people questioning how he managed to sneak through a perimeter but no one is questioning how he managed to do this right in front of the guards without being noticed?!). Also, why did Miranda Tate keep her involvement a secret if the whole point of it was to hurt Bruce Wayne - they didn't expect him to escape, so as far as they knew Gotham would be destroyed without him ever knowing. What did she plan to do, dramatically reveal that she's Talia on camera, so that Bruce Wayne could learn about it in prison (well, if he hadn't already destroyed the TV)? To me it's things like that that are the plotholes and stretches of suspension of disbelief - not the fact that Bruce Wayne travelled to America in a couple of weeks and snuck past some guards without a scene explicitly showing us that.