Heat and voltage are two things to check. (If the power pole plug is really bad, the black plastic plug in will be discolored, or or burned looking, look at it closely,)If the plug is hot under load; A/C, hot water heater, (hotter than ambient) AND the voltage is lower than with no load, these are indicators. But, unless you have benchmark numbers, it is of little value. I can check the voltage on a line under load and get two varied readings with an inexpensive meter, then check it with my true *RMS Fluke and get different readings.
No easy answer, but heat and lowered voltage are things to check.
I bought 2 simple infra-red handheld meters at Radio Shack a few years ago for toys, cheap ones, but they work rather well. I think they were under $25.00. Might be a good instrument to have. I have a good one for my commercial work I use, most of you would not need the commercial unit.
As far as instruments, my suggestion is to buy a good one, there should be no joy in purchasing a $10.00 electrical multi-meter to check on our your $60,000.00 Montana. Remember;
'The bitterness of poor quality remains, long after the sweet taste of the cheap price is gone.'
I like the digital Craftsman DC/AC clamp on meter #82062.
It can check amp draw, both AC and DC, with a hold feature on the reading, it will check your flashlight batteries, car batteries, line voltage; 120 volts, 230 volts, fuses; Ohms.
The Craftsman is Second choice to my Flukes of course, but they are more suitable for my occasional repairs for paying customers.
I'll get a picture up for anyone interested.
*
True RMS
Ozz