Other mistake: Angel implies that Wesley told him the device will kill Illyria. But this Angel is from earlier in the timeline, as shown when he tries to tell Wes and Spike things they have just told their Angel. So Wes did not tell this Angel that the Mutari generator will kill Illyria. Angel should know nothing about it.
Character mistake: Angel comments that Vanessa was acquitted because of a hung jury. A hung jury means the jury couldn't come to a unanimous decision; the case would require a new trial, while an acquittal means the jury found her not guilty, and she couldn't be tried again for the crime.
Revealing mistake: When the gang attack the vampires in the bowling alley, watch as Jasmine and Fred walk over the bowling lanes in the background as the others fight the vampires. Jasmine slips on the floor but manages to maintain her balance. You'd think a deity with superhuman strength, telepathy, shape-shifting and psychic capabilities would be able to walk on a smooth floor without slipping and also know that it was smooth to begin with. Although she may lack friction, the shot should have been re-filmed as it is a blatant mistake.