Aioli used to mean "flavored mayonnaise" --- I will accept several versions of aioli, all of them made largely from garlic, and I am perfectly OK with several regional spellings, but I will not accept "our house special smoky chipotle aioli." (Incidentally, I'd have to disagree, just slightly, with the person who objects to uses of "pesto" that don't include basil: there are legitimate arguments to be made for sauces to be called "pesto" that are not pesto Genovese or much similar. But in principle, yes, I agree with you.)
"Our" anything --- I dislike the use of first person plural pronouns on menus, especially chain restaurant menus.
I have had it up to here with signature. As far as I am concerned, nobody has a signature dish unless he or she has written on it. I don't care if you invented it: Paul Bocuse may not claim the truffle soup he invented as his "signature dish." The notion was bad to begin with, and is now bankrupt. "Chef's special" can stay, because it is hallowed by age.
Most of all, I hate the word authentic. I don't care if you were taught to make the dish standing beside the ultimate old grandma from wherever. The only dishes of which you can properly say they are or are not "authentic" are ones that are in some sense clearly defined or regulated. If you really want to say you are serving "authentic bistecca alla Fiorentina," I'm OK with that, but you'd darn well better mean that you obey to the T all the local precise regulations in Florence about that dish. If you really want to claim certain French dishes this way, fine, I guess, but why not just say "made to Escoffier's recipe" or something like that? It's funny: nobody ever wants to claim that they're making an authentic French haute cuisine classic, because they're too busy claiming that something is "authentic" Mexican, Chinese, or Indian food, which is almost totally oxymoronic (and without the oxy-, too).