We've already covered that you mustn't eat after the Queen stops eating at dinner. You should also refrain from speaking to her if you're sitting on her left-hand side at the table. An archaic tradition dictates that at a formal dinner, the Guest of Honor sits on the right of the Monarch, and so the Monarch will greet and make conversation with them first before turning to speak to the person on their left.
Formula 1 racing driver Lewis Hamilton recently fell afoul of this tradition, having been invited to dine with the Queen. Sat to her immediate left he tried to strike up a conversation (a bold move in any circumstances!), only to be politely told that he should talk to the person to his own left first, and that the Queen would be with him in a moment.