Check for a ground current leak down your shore power cord, and also check for a DC leak on YOUR boat.
Both are entirely possible and both will cause your zincs to be eroded at an accelerated rate. The latter can be a LOT of fun to find - the easiest way is to shut off EVERYTHING and turn off ALL DC breakers, disconnecting the batteries. CHECK WITH A VOLTMETER to make sure there is NO VOLTAGE on the system (you'll destroy an ohmmeter if there is voltage!)
Now set your voltmeter to OHMS and put one tip on the POSITIVE DC lead that you disconnected from the battery. Put the NEGATIVE on the BONDING SYSTEM of the boat. It should read OPEN (infinity.) If it doesn't you have a leak somewhere in one of the primary circuits in the big panels (e.g. engine starting circuit, charger, etc.) Fix any current leak found there.
Now start turning on breakers. The meter should remain on INFINITY. If it shows a resistence you have a leak. It is possible that the "leak" is in fact a soft power switch on some piece of electronics, so you have to run down EVERY indication of leakage to see which ones are real and which ones are not, and disconnect the V+ feeds on the electronics that have soft power switches as you go.
Fix all leaks until you get to where ALL DC breakers are ON, all DC loads are OFF (light switches, etc) and the meter reads OPEN (infinite resistence.)
Common sources of leaks are wires that are immersed in bilge water (bilge pump switches are notorious for this), have chafed partially through, or are on a terminal block that also carries ground and has corrosion, moisture or other material that can "bridge" the two sides.
For the AC side if you have an ISOLATION transformer then your AC Ground (from the pedestel - make sure you unplug it!) should NOT have continuity to ANYTHING (including the bonding system) OTHER THAN the shield at the transformer. That is, the SHORE ground should STOP before it gets on board. If you have a NON-ISOLATED AC system then the grounds are TIED and if there is an offset on the AC cord coming from the shore ped you have a problem. You can install a ground isolator but IMHO the better solution is on a boat large enough for a transformer is to either replace or reconfigure that transformer to be an ISOLATION transformer and never worry about it again, nor worry about the risk of the ground isolator failing and electocuting someone.
