What are physical signs you might need to replace your brake rotors and how long should a new set last?
Screeching/grinding while braking.
Vibration/shaking in the steering wheel/brake pedal while braking.
Brake life depends on your driving conditions/style.
Tester
Visually, they’d include glazing and/or grooving if the rotor surfaces and warpage. A shop would measure for warpage with a “dial indicator” that measures the variation back & forth of the surface as the rotor turns (lateral runout) and in a vented rotor he’ll likely use a micrometer to measure variations in the differences in distance between the two rotor surfaces. He’ll also measure the thickness of the rotors IF machining is an option, to be sure there’s enough material to doo so safely. Measurements, however, are generally unnecessary if the rotor is visually bad, and only necessary for verification if the car pulsates during braking.
Here’s a link to some photos you might find illustrative. One of them shows a vented rotor with one side completely worn off. That one needs a new caliper too. 
https://www.bing.com/images/search?q=photos+of+bad+brake+rotor+surfaces&qpvt=photos+of+bad+brake+rotor+surfaces&qpvt=photos+of+bad+brake+rotor+surfaces&qpvt=photos+of+bad+brake+rotor+surfaces&FORM=IGRE
if you replace the disc pads yourself, the rotors should be replaced at the same time. Otherwise, you need to take the rotors to a shop for resurfacing. The cost of resurfacing is so close to the cost of new rotors that I prefer new rotors. An added bonus is that you get the car back inactionmuch quicker with new rotors.
Also pitting or cracking of brake rotors would be another flag. A new set should last the life of the new pads.
Also as some rotors wear down and become thinner, they can develop a ‘rim’ on the outside edge where the pads did not wear the rotor down.
What about color? I was told that color or discoloration is proof of need of replacement.
Blue color on the rotors indicates hot spots.
Which means the pad’s and rotor’s aren’t happy with each other.
Start over.
Tester
I looked at the rotors and I don’t see any “blueing” on them I will try to get a picture here and post them. The rear rotors are not even a year old, so “supposedly” they are covered under warranty still, but what baffles me is I have had 3 places check the brakes and it was just the most recent check that said anything about discoloration on the rotors, the two other places said they saw nothing wrong and couldn’t explain the random grinding sound I get from the right front brake from time to time.
It might be helpful to know why you are asking. Is it the random grinding sound? Or what you think was an inferior brake job? Other?
On a random noise from the front brakes, my first suspect would be the flexible rubber hose going to the caliper. Took me forever to figure that out the first time it happened to me 40 years ago; I’ve had it on multiple vehicles since. The rubber wall can collapse and cause the brake fluid to hold pressure against the rotor. And, it can be intermittent when first failing.
I will hear a “grinding” sound coming from my right front brake from time to time. Usually if I am having to brake hard and fast, but even then not always. The front brakes were put on in Nov of 2014 right before I bought the car by the dealership (I got the paperwork from them when I bought it). The rotors look fine, to the touch there isn’t any rigged feel to them and it’s only coming from the right front.
Might be a bad wheel bearing. Might be ABS related. Could be a ‘cocked’ caliper. …
Put your make model year etc. on here.
Its a 2003 Impala with about 126,000 miles on it.