"that orange notice i received with my new flashscan v2: it says 'do not connect flashscan between a vehicle and a personal computer or a laptop if that computer is being powered from the vehicle's 12 volt system through a power inverter' "
Do not connect FlashScan between a vehicle and a laptop powered by a power inverter
(This discusses using an automotive diagnosatic tool, connected to a laptop and the vehicle's electrical system)
(Note: simple resistive devices like heating pads do not have a power supply and are not in the category of "sensitive" equipment)
If considering recommendations made by others, also consider these facts:
There are several reasons why "sensitive" 120vAC electronics should not be connected to a DC-AC inverter, but in addition to the grounding issue, affordable inverters do not output true sine wave AC power; instead, they output a stepped approximation of an alternating current sine wave. The result is stress to the power supply in the 120vAC equipment connected to it, and in most cases, you can actually hear that stress by noticing the slightly different sound when an AC power supply (such as in a PC) is running of off inverter power compared to 120vAC from the local utility. In most cases, the power supply in electronics equipment converts the 120vAC back to one or more DC voltages. It's not difficult to understand that converting DC to AC and then back to DC is not the most efficient way to do things. Also, an inverter draws power from the vehicle (alternator or battery, if it's not running) even when no AC load is connected to it. Some inverters automatically power off to prevent most of this no-load power consumption. The efficiency of inverters also decreases with less AC load. In other words, if you have a small AC load connected to an inverter capable of handling a much larger AC load, the net efficiency of the system is lower than with an inverter sized for the load. Typical 12vDC inverter efficiency is only 80% to 90% if properly sized for the load, and much lower if a large inverter is used with a smaller load. The end result is higher power consumption from the source that has the less available power (e.g.: a 12v car battery), and this is more important if running larger loads (e.g.: electric blankets) when the vehicle is not running. Conversely, when connected to 120vAC power, there is no stringent limit (except for the circuit ampacity and/or the power cost). So the best approach in terms of efficiency (which reduces the load on the vehicle battery) is to use DC equipment in a vehicle, and use a DC power supply (e.g.: Schumacher PC-6 6amp 12vDC power supply) if need be to power that equipment from household 120vAC power.