I used to be in vending.

For bills and coins, I count by object, not denomination. Then multiply total by denomination.

For counting large numbers of bills, I like creating stacks of 20. Then I count the number of stacks. After that I make stacks of 100 bills, and wrap them. In this way, I am never 75 bills deep, lose count and have to restart.

I know I have to count each stack of twenty twice, and ideally not three times, so I count 21 bills out, then if its 21 the second time, I take one off.

For piles of coins(and socks, et al), remove the most common/visible/largest type. For example, I would remove $1 coins into their own pile/bag, not bothering to count yet. Then as they become less obvious, I switch to $2 coins, then $0.25, then $0.05(since they are larger than $0.10 coins).

I had an electronic coin counter, but away from the office, that's how I sorted coins. If I wanted to count on site, it was a lot easier to count homogeneous bags. I could also weigh for a rough estimate.