My grandson and I did tech support for a big cross state ride in the middle 90's.

The most common technical issue, as you might expect, was flat tires.

The second most common problem was broken spokes. I suspect that's less common than it was then but I think it's still probably a fairly common issue.

The third most common problem was trashed bottom brackets. Since that time I suspect that sealed cartridge bottom brackets have greatly reduced that occurrence.