Modified sine wave inverters dump out about 24% of their power as non-60 Hz harmonics. That's why electric motors, transformers, and some electronics sometimes buzz and a few will eventually smoke. IEEE power standards call for no more than 5%. The "timing" of the motor is keyed to 60 Hz, and the rest goes where it goes. Sometimes the off-harmonics will deliver a little bit of power to the motor, and some motors are more resistant than others to the off-harmonics. A lot of electronics just don't care, because a wall wart is converting back down to 19 VDC anyway. But some electronics care very much. And of course heating elements don't care at all.
Most things are just fine running on modified sine waves, to a point. It may come down to something subtle like a refrigerator lasting for only a year on MSW power, as opposed to 15 years on PSW. If it gets you through a two week outage, then MSW's not a problem. Planning on running for years, could be a problem.