Uber can easily compare image hashes so no image of vomit can be used for more than one claim. That should keep out less technically savvy fraudsters.
They could also demand a scan of a receipt from a cleaning place, and then verify via GPS traces that the driver actually went to the place after the supposed incident but before taking the next ride.
Uber should also make a notification or popup for the customer if they are charged extra after a ride. An "appeal" should be possible from the notification.