It's been awhile but my grandson and I did tech support for a cross state ride in Missouri.

1. By a large margin was flat tires. We ran out of replacement tires and had to buy some additional spares at a local shop.
2. Broken spokes.
3. Surprisingly was bottom bracket issues. That, however, was before cartridge bearings became as common as they are now. We had some bottom brackets with us and used them all.
4. We replaced several shift cables.

One fellow came to me with both shift cables positively "hairy" where they exited his shifters. I don't understand why they hadn't broken. I asked him "When you signed the form that said your bike had been serviced prior to the ride, what did you think that meant?"