When Jim brings Kara to her room after the lake party it is late night however shots in her bedroom show daylight outside. The following scene when Jim an his friends leave the house, it is dark outside again.
On the way to Jim's old house, as the car drives past you can see Michelle wearing sunglasses for a split second, during the conversation about "the incident" they are nowhere to be seen. Later when Michelle steps out the car to hug Jim's dad, they appear on her face again.
Once Jim arrives back to his Dad's home it is clear that its not the same house from the previous films. The walkway is different along with the yard layout. Also the house next door is no longer brick as it was in American Wedding.
Finch tells Selena he "doesn't consider" French Guiana a country. It's irrelevant for Finch to say that because French Guiana in actuality is not a nation. It is an overseas department and region of France.
When all the guys meet in the bar, Selena shows them the YouTube video from 1999 with Jim dancing for Nadia on her smart phone. This isn't the actual video from Jim's web-cam, which is in the corner of the room. She used footage from the first American Pie movie itself, which is not possible.