Reverse polarity means the hot and neutral wires have swapped somewhere between the dock pedestal and the boat's panel. Lights still light and the kettle still boils, so nobody notices. The danger is in what stops working: breakers are designed to interrupt the hot wire, and with polarity reversed a single-pole breaker switches the neutral and leaves the circuit live.
What the standard asks
ABYC E-11 asks 120 V shore power systems for a reverse polarity indicator: a light or alarm that signals continuously when polarity is reversed. As quoted on the SailboatOwners forum, its impedance must be at least 25,000 ohms, so it draws less than the 5 mA that trips a standard US GFCI. It's wired between the neutral and the safety ground, which is why it lights when the neutral is live.
How a surveyor checks it
With shore power connected, look at the panel for the indicator and whether it's lit. Then test. A plug-in polarity tester at the dock outlet tells you whether the fault is ashore; the same test through the cord and at the boat's inlet narrows it down. A meter from neutral to ground should read close to zero.
Boat Blurb's procedure for a lit indicator: unplug immediately, check the plug connections, test again with a cord you know is good, replace the cord if the light goes out, then check the pedestal, tell the marina and check the boat's panel for loose connections. A faint glow can come from resistance on the neutral path, a corroded connection worth finding before it heats up.