Unless things have changed dramatically, my one tip is to bring nice clothes for the Commencement Ball if you've got them. Men are mainly in suits and women in cocktail attire or dressy suits.
I'm a parent now, so I hate to say it, but let your child have space. Graduation was extremely emotional for my core group of friends and I suspect for almost everyone else. At a school like Yale, people scatter to the four corners of the world and bittersweetness is very heavy in the air. To this day, it is magic when my entire gang gets together, but it happens very, very rarely and we were all aware that this would be the case over commencement weekend.
Oh, and parents sit and wait for graduates to file in.