To address the problem, first we need to understand how the flush mechanism in the Dometic 300 series toilet works.
There is a water valve on the back of the toilet, a spring actuated flush pedal attached to the valve and also attached to a curved "ball" that seals the toilet bowl to keep water in the bowl and to allow the water/contents to "flush" when the foot pedal is pressed. The spring on the foot pedal returns the pedal to "normal position" and also mechanically forces the "ball" back to the closed position. The water valve opens and closes in conjunction with the foot pedal.
So, if the spring loaded foot pedal is working properly, the water valve and the "ball" will also operate properly.
The only two problems would be either the "ball" isn't closing (which would also keep the water valve open) or the spring isn't pulling the mechanism back to the closed position.
Usually, the rubber seal around the "ball" is the culprit. As stated by SmittysRV, the "ball" isn't returning to the closed position. He goes on to state that lubricating the rubber seal caused the toilet to work properly for a while, then it again failed. I wouldn't think the spring assembly in the foot pedal is the issue based on this fact. So, the seal is most likely the problem.
Dometic has a procedure in the owner's manual concerning this problem. It states:
IF NEW TOILET DOES NOT HOLD WATER IN BOWL… Please follow the procedures below before attempting to replace the seal. 1. Hold flush ball in full open position by pressing on pedal. 2. Using finger, apply moderate downward pressure around edge of ball seal. 3. Close flush ball. 4. Keeping flush ball closed, pour one quart of hot tap water into toilet bowl. 5. Let water cool completely. 6. Check for leak. If leak still persists, flush ball seal should be replaced. Follow instructions provided with replacement seal kit.
I would try to "reform" the rubber seal and see if it will allow the "ball" to function properly. If not, then I would purchase a replacement seal and install it. The seal can be installed without removing or disassembling the toilet, so the only thing required is a new seal and a pair of rubber gloves.
If the hot water and/or a new seal don't fix the problem, then it's the spring on the foot pedal not exerting enough "return force" to close the "ball". That's probably not the issue and I'd think it's a "last resort" kind of repair.
DO NOT take the toilet apart at the base/bowl joint. It is not to be separated in the field and there are a number of warnings about not taking the toilet apart at that joint.
Here's the link to the toilet owner's manual:
http://www.dometic.com/enus/Americas...ation-Manuals/
Scroll down to "toilets" and select the first link.