The piercing is on the left side of Megan's nose until she goes dancing. When she gets back into the blanket fort, it's on the right. After they leave the fort, it's back on the left side again.
When Alec first looks at the magazine page Megan threw in the toilet, the page folds over revealing that he is reading point #3 of the article. When the camera angle changes, the page has flipped, and he is now reading point #2.
Megan explains that she has a pre-med degree from NYU that she doesn't plan to use because she does not want to go to med school, thus rendering her degree useless. In reality there are no such things as pre-med degrees, certainly not at NYU. Pre-med is a set of courses or a program you have to complete in addition to your major if you wish to apply to med school. So she would have in reality had to have some other degree which would still be useful.