Yes, it has a flue (sealing to protect from green water--you MUST remember to open it), separate combustion air supply (ABYC suggests a separate sealed compartment, which it has; this is a very difficult requirement for most boats), leak detector, and flame interlock. It works well... sort of.
a. Showers always go through a lot of water, but more so when using hot water, because of the time required to heat the pipes and adjust the temperature.
b. It really doesn't work so well for galley hot water, for the same reason; the waste each time is OK at home, but unacceptable even on a boat in a marina. I end up always using cold water for dishes. Thus, I DO NOT leave the unit on unless I am taking a shower.
c. The temperature regulation is not perfect, not quite like a tank. To get steady temperature you need to let it run wide-open, which wastes more water, even for the fastest shower taker.
d. A hot shower put TON of moisture into the boat. This is never acceptable, summer of winter. While a bathroom fan helps, not enough.
b. When on the hook in the summer, take cold showers on-deck (we have a transom shower and use it a lot). This can be done discretely in the cockpit, wearing a bathing suit for the most part. The water is not really cold on a boat, since the pipes are not underground.
c. I don't care for solar showers; if it's warm enough to work well, I can take it cold more simply.
If I were living aboard and could manage the space, I would go for a small engine-heated electric tank heater. If it had to be propane on-demand, make sure the installation is faultless. And I would use marina facilities most of the time.
Before you consider going for a ventless heater--the OP did not suggest this but many have in the past--realize that a hot water heater has a HUGE firing rate compared to the stove: 199,000 btu vs. 8,000 BTU. These MUST be vented in a small place like a boat. There have been several cases reported of sailors getting knocked out while showering.Propane possible boat peril One sailor died, another sickened while in shower - Baltimore Sun