Technically, this is not a "food mistake" but the way your date speaks to and treats your waiter is a great indicator of who they really are as a person.
It can be incredibly rude to order for someone without giving them fair warning that you're going to do so. If you take a date to your favorite restaurant and really want them to try the house specialty, suggest this idea at the beginning when the menus are first handed to you. If your date is game, go for it. And if the dish is a big hit, it will certainly come off as impressive and you'll be able to let them order for you on date two!
Fess up as soon as you can! If you've already made it to the restaurant before realizing this, eat a piece of humble pie as an appetizer and make light of having to sit at the bar while you wait for your table. If you haven't yet picked your date up, go with Plan B! Head to the grocery store for some picnic staples and have a date night al fresco.
It's not a bad idea for the initiator of the date (the one who said "will you go on a date with me?") to reach for the check first, guy or girl. But if the other person has serious objections to not splitting the check on the first date, just go Dutch! Nothing stops a date in its tracks like an awkward and unnecessary disagreement.
Don't get too wound up about it, at the end of the day it's not that big of a deal. Make a joke of it and be able to laugh at yourself for your flub. If you spill on your date, offer to get them some seltzer water to help clean it up.
This is a pretty tough one to recover from! I would say abstinence is the best policy here. Avoid foods that have a tendency to get stuck in your teeth, such as raw broccoli or anything with seeds, so you won't have to worry about the problem to begin with. If something does get lodged in your chompers, DON'T try to remove it while you're at the table. Excuse yourself, and hope that you noticed before your date did. If they start to pick their teeth, offer them a toothpick. If they don't get the hint after that, it's probably time to go home anyway!
If your date is encouraging you to try something new and you're not 100% sure how to eat it, don't be afraid to ask them for help. If the sparks are already flying, it could be super romantic to have your date teach you the proper methods and feed you a piece!
Suck it up (no pun intended) for the remainder of the date. If it really grosses you out, don't plan to go on a second one with this person.
Find two appetizers (or an appetizer and a salad) that are more appealing to you than the entrees themselves and make your meal out of that. Try to be as easy about it as possible so that you don't come off as picky. If there's absolutely nothing on the menu that you can force down, jokingly ask to try somewhere else. You can say something along the lines of "This place is too fancy for me tonight! Let's try that great new food truck, I hear they're parked just around the corner!" For date two, suggest a restaurant that appeals more to your own tastes, and hope your date will like it, too.