I assume the output of my 2003 generator is giving me dirty power.
How do I determine this......
Your assumption is unfounded, unless you prove different.
Practically ALL generators are fitted with voltage regulators,
to deliver consistent power output.
To determine, research your generator model number for
specific info on voltage regulation, either in the manual
or direct from the manufacturer.
The furnace electronics will be more susceptible to spikes
and surges, and a simple surge protector on the line should
alleviate any problems in that department.
Furnace is no different, BTW, than your microwave, TV, cable box,
alarm clock, etc., etc.
You're overthinking, as long as the generator supply
is well over the wattage of all the stuff you're gonna run.