One plot error i always thought was funny...

He told her that he was required to go to therapy at the hospital. She brings it up during the carnival scene.

"So it goes" -Slaughterhouse Five

Yeah, what he said, she brought it up at the carnival and she seemed frustrated with him, asking why she couldn't go with him and he said he didn't want her to see him that why. I think they had the converstation several times before, and she would let it go to enjoy their time together but when it got brought up it was emotional. I didn't take the scene to mean it was the first and only time it was brougt up.

As the others have said, they do imply that Peyton keeps making excuses about needing therapy, like when he says that the hospital didn't let him see her because of his accident, just vague excuses.
In the carnival scene they really hammer it home with Peyton insisting that he leaves for his therapy session again, which is obviously beginning to aggravate Julie.

The crazy part is that I finally realized.. why didn't he just go see her during the nighttime? It woulda made a lot more sense if you think about it in the grand scale of things. His mask wouldn't disolve out in the night (in part 2 it stays on fine,) so he would be in no hurry unless he is inside somewhere with a ton of light, and two his alibi would make more sense. People rehab a ton in the daytime at hospitals and he could say he's having serious therapy or something it would make much more sense than him running away after 1hr and 30 minutes at a time. The whole thing looks stupid in hindsight after you've seen the sequels.

I honestly don't know what Rami was thinking there.. granted the carnival scene might not have happened but I'm sure there woulda been a chance to reveal his true self to her eventually.