Mabel says she thought high school would be like a musical, a clear reference to Disney's popular series of 'High School Musical' movies.
If you look at the calendar on the wall in Dipper and Mabels room, the date she has circled is the 5th Friday of August. Since this episode was made in 2015 that would make their birthday August 28th however on the birthday invitations it says August 31st. However, the summer is during the summer of 2012, because that's when the first season aired, and the 31st of August was a Friday in 2012.
The invitation for Dipper and Mabel's party says their birthday is August 31st, making them Virgos.