I'm embarrassed not to know the answer to this but here goes:
On my A/C panel there is a breaker for the battery charger. I've been leaving it on all the time when the boat is plugged in. Is this the correct thing to do? Or should it only be on until the batteries show a full charge?
The answer, like most things, is "it depends"... Many chargers that claim to be smart are not in-fact smart at all. Some will bump out of float at the slightest hint of current being drawn and others have higher thresholds or don't simply reset an
egg-timer when they do revert to absorption.. Many chargers use an
egg-timer approach to determine transitions from absorption to float and this may not be ideal for your bank. Many chargers lack remote temp sensing and you can very easily be over charging a warm battery even at float voltages.
Many chargers have very, very poor low current capabilities which leads to the power supply pulsing on and off so as not to over shoot the voltage sent point however they do with every blip and this causes excess heat. When they "pulse on" they do over shoot then turn off then pulse again. Many chargers also have poor AC ripple which is a complicated subject especially when VRLA batteries are used. The Sterling PCU and ProMariner Pronautic P have some of the lowest ripple out there at just 14mV....
Long and short is that I have seen batteries destroyed in a year or less by poorly designed chargers. If you run refrigeration or any DC loads at the dock it is best to have a charger that allows a setting to lock the charger into float mode to prevent cycling between float and absorption.
That said if your boat has parasitic loads at the dock then running the charger will nearly be a requirement. If you eliminate parasitic loads and turn everything off then charging to full and turning off the charger can sometimes be a healthier approach, if your charger is not up to snuff. Unplugging from the dock entirely and using solar is by far the best choice in terms of corrosion potential...
Not an easy answer...