This is the first time when the TV credits in the opening sequence were modified.
Marge says the mental hospital Diggs will be staying at is an Arkham Asylum type place referencing Arkham Asylum from the DC comics.
One of the names written on Diggs' cast reads John Swartzwelder (a long time Simpsons writer.)
The idea of Bart eating things for money may have come from an old chalk board gag in Marge vs. the Monorail saying "I will not eat things for money".
Diggs name could possibly reference Daveed Diggs, but he has never appeared on the show nor does the character look like him.
Diggs is probably 11 years old, but to get a falconry permit, you have to be at least 14 (and supervised by an experienced falconer for the first few years). Like the bullies, he could be older than he looks or he likely lied about his age to get a permit.
Even if Diggs is older than he looks, the club would be too expensive, and it's very unlikely that the school would allow a club with only one person in it to exist.
Lisa eats Bart's taco that contains meat without even thinking about it, even though she is a vegetarian.
When Bart goes home, his backpack switches multiple times from both shoulder straps to one strap.
Falcons don't "bring" their catch to the falconer.
At the falconry event, you can see many birds of prey flying free. In real life, they would attack each other.
The whole plot of "setting falcons free" is not realistic, as they would return to their owners as they are trained to do.
As Bart starts eating the frog, it is light grey, but, in the next shot, the frog's color is dark green.
"The Tardis" is one of the names that Diggs wrote on his cast. The TARDIS is not a person, it's a time machine used on the show "Doctor Who".