AC duct leaking

Most likely the ducts were not sealed properly at the A/C unit and/or the various registers. To check the unit connections you need to drop the ceiling assy. of the unit. To check the registers; generally the louvered portion pops out. Any gaps in the connections can be sealed with metallic duct tape available at HVAC or plumbing supply houses.

The gaps can be sealed from the inside? How would I reach them? Or do I need to cut into the ceiling?

Most ceiling registers used in RVs have a louvered section that will come out. Once that is removed you will be able to see where the assembly attaches to the duct work. That is where it is often not sealed well.

Before cutting the ceiling buy some HVAC tape at Lowes, Home Depot, ACE or wherever. This is not standard dollar a roll Duct tape. Here's a link to Home Depot.
Link

Pull every register down and carefully seal the gap between the ceiling and the duct. Then pull the inside cover off the AC and seal up all the gaps you see. Then see if there is an improvement.

just use aluminum hvac tape and use it to both seal the gap and pull the duct down even with the ceiling.

what you found is a pretty common problem with RV HVAC systems