Couple things. Every official counts offense or defense and gives a closed fist signal to the others counting the same team to saying they have 11. Ideally all officials give and acknowledge those signals. If a team has 10, I show an open hand. THere is no signal for 12 -- the officials are counting again and, if it's confirmed, throwing flag.
If the down and distance is less than fourth and more than 10 yards (does that make sense) some will cross their forearms in an X to each other as a reminder that the ball has to pass 2 stakes before you stop the clock.
Most associations use a rolling fist when a scrimmage kick is coming -- especially if it's a field goal attempt -- as a reminder that a grounded kick is still a live ball.
On my crew we have a signal when there are very close to 5 yards to gain a first down. On every chain is a piece of tape at the mid point, five yards from the stake. THe linesman will look at the box and which side of the tape that's on and give me a signal that I doubt anyone else would ever notice -- just a hand on his chest. That signal tells me whether a 5-yarder on defense (encroachment, illegal substitution) will result in a first down or not.
Another one i can think of but no longer use: In years past, the umpire would hand the ball to the kicker and ask if the kick was going to be an onside kick. If it was, there was a signal for that. I won't say what it was in case someone out there is still using it, but when I started officiating, my first association's signal was for the umpire to scratch his butt (rub his hip more was more common). It was a little way we entertained ourselves.
I say we don't use that anymore because with most places now using seven officials, if there is an obvious onside situation, the officials move to cover it. If it's not an onside situation, the coverage areas are precise enough that we are able to act as if we are expecting an onside kick every time. Back when five guys had to cover the entire field, you didn't really have the luxury to change much in positioning, so you had to be more aware and a tip off of an onside kick was more helpful.