LPG fired tankless waterheaters have been popular in European boats for some time. There was a time about 35 or 40 years ago, it was popular in the US. Unfortunately there were some deaths from these water heaters. These involved carbon monoxide. Many of these waterheaters were improperly installed, and not properly vented to the outside.
It is difficult to comply with ABYC and put in a full time tankless water heater. The gas stack has to be vented to the exterior, where no exhaust gas will come back into the cabin. You want "bilge sniffer in the deepest part of the bilge (since LPG is heavier than air) and in the compartment where the waterheater is installed. It should not be installed in the engine room. There should be an auto shut off if the sniffer alarm goes off, and a control valve to shut the LPG off at the tank when you are not using the tank. Then you have to put a sealed, vented overboard, place for the tank (where fumes are not likely to get into the boat--and then route the hoses into the boat. If the boat already has a propane or LPG system for a stove, then this is easier.
I have owned a number of boats with LPG stoves, and the full safety systems, and one boat with the LPG tankless water heater. I would not own another one--but that is a decision based on personal safety concerns. If you add one, you should check with your insurance to see if it and the installation will be accepted!