Ferris could have easily - and plausibly - avoided detection at the parade by wearing a "carnival" mask. Of course, thanks to his being The Ace (see main page), he pulls it off anyway.
Obviously it's a comedy so it's something that wasn't worth addressing, but how the hell did Cameron get away with wearing a Detroit Red Wings jersey in the middle of Chicago? It's one of the most bitter rivalries in North American sports.
Cameron's being able to wear a Wings jersey in Chicago maybe lends to the theory that the events of the movie are all in Cameron's imagination.
Or, they're planning on releasing an alternate ending where Cameron is savagely beaten or murdered for wearing a Red Wings jersey.
The art museum scene might at first glance just seem like a playful montage of teens goofing off in an art museum, but one element stands out; Cameron's fixation with the George Seurat's "A Sunday Afternoon on the Island of La Grande Jatte". The famous sequence features alternating shots of Cameron and the painting each one closer then the last until at last it zooms in on a single blotch of paint. One might dismiss this scene as just a portrayal of the fun of impressionist paintings, but considering the subject matter of "A Sunday Afternoon" it seems more likely to be a key moment for Cameron's character. The painting shows people arranged as though on a chessboard all facing right angles. The exception to this are children and animals who are shown frolicking freely and naturally in the scene. The intent of the painting was to criticize the rigid social constraints of Victorian society. The exact spot Cameron is staring at is the face of a little girl. Unlike the animals and the other child in the picture this girl is walking with her mother, holding her hand, seemingly pulled into the rigid pattern that all the other painted characters are trapped in. Considering Cameron's relationship with his parents this seems like a very relevant thing for him to be fixated on.