Deliberate mistake: When the Trunchbull is drinking from the glass with the newt in it, you can easily see that she doesn't actually drink anything, as the water level stays exactly the same. Logical, as the newt is real, but it's still very obvious because she drinks for about 15 seconds. (00:46:55)
Deliberate mistake: At the end just before the president is killed he fixes his tie, but it keeps on getting fixed to messed, to fixed, etc. Deliberate homage to "A Few Good Men", but worth looking for nonetheless. (00:28:15)