what are the most common things that break?

While on workcamping gig Delta faucet on Kitchen sink started leaking like a fountain. Turned off water and water pump to stop, went to Home Depot for repair kit, and some silicone grease. Repaired with the wrench included in repair kit.
Biggest repair while travelling was replacing 27" boat anchor TV with a LED flatscreen. Had to get two neighbors to help get it out due to weight. Garbage dump charged me $15 to take it. If DW had stepped out of car before first weighing, we could have gotten out free. That thing weighed almost as much as she did!

A lot of what breaks is the cheap plastic parts like electrical cord doors, range hood vent doors, etc.
The there's all the bearing issues. It is handy to check your wheel temps when you stop and have a brake spoon, extra packed bearings and a can of brake cleaner in case you have to do a repair on the road.

The battery powered clock we hung on the bedroom wall seems to like the floor best. Currently we have less than half the original clock stuck back on the wall, but its still functional. When it makes that final leap to its death we'll give it a proper burial. Until then we continue to give it counselling.

The only thing I can think of that broke was the cheap crappy plastic stove hood vents. Replaced it twice and it was broken again when I sold it last summer, and I didn't even use the thing. So put one in your tool kit along with a roll of butyl tape and a Philips head screw driver.

In reality, I carry tools for electrical and mechanical issues, and not a vent flap.

Promises.

Only thing that has happened to either of my TT while camping, Is the sink elbow came loose. I tightened it back up with the channel locks, and goo to got.

Everything else, I do at home. I check out the TT each spring before the first trip.

Aluminum bed frame broke to pieces on last outing. Went to Home Depot and got plywood sheet cut to fit. Had an extra cut to get it in toad. Couldn't have it fixed till we got home. Carry small tools for small problems, no way to carry everything needed for big problems, so don't even try.

Screws loosening up would be #1. If you drive on bad roads, use the cupboard doors to much or put the shade up and down to much, a screw will come loose.

if its made by man it will break so pick 1 or 2 or 5