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 first few years). Like the bullies, he could be older than he looks.
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's a 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".