In our Roadtrek (Class B) we have an inverter that is used just to run the TV and the DVD player. We think it wrecked the TV. When I put our electrical checker on it there were just 101 volts and ther...
101 volts is probably due to MSW and is normal. Open neutral is also normal and will not hurt a thing. Most tvs have a brick to supply lower DC to the tv. Have seen some things run hot on MSW although for this it should not be an issue. Signal interference might be a bigger trouble but maybe not with digital signals today.
Anyway I recommend a 200 or 400 watt Go Power sine wave inverter.