All the catalog fundraisers I've seen include envelopes where the parents usually fill out the amount of money that they have enclosed on the outside, and the inside includes all the order forms. Depending on the organization, we keep either a copy of the order form or the envelope (usually a copy of the order form).
At our bookfairs, we do issue receipts. They're usually standard receipt book forms with carbon. They're not very detailed (as in there's one line marked "books" with a total), so they can be done quickly. If the books are paid for with a credit card, we don't write up another separate receipt for that; we only write up the receipts for cash/check sales.
For events like bingo, we keep the initial reservation forms that show how many food tickets people ordered, how many bingo books, etc., because most of that stuff is sold pre-event. That money is all deposited before the event even takes place. But at the actual event, for any extra bingo books sold, concessions, etc., we don't issue any receipts for that. Same thing if you were to have a carnival and have people buy individual tickets for food, games, etc. Or concessions at movie night. But, if you use a form at the end of the night to show where two people counted the cash that came in, and attached that as your documentation, I think that's perfectly reasonable. It's not like the IRS expects you to go out and buy cash registers so you can have register slips to document your sales.
I wouldn't worry about documenting every little thing, but if you can get the bulk of your big events covered in some fashion, you should be ok.