uh.... first thing to check would be shell quality, for cracks, or how porous it is. a porous egg when a light is shone into it, has lots of lighter spots in the shell. the problem with a porous egg is it will loose humidity faster than a non-porous one. and also it is easier for the egg to be contaminated with bacteria.
the only real way to tell if an egg is fertile is either by cracking it open (which means no longer hatchable) or set it and wait for something to happen. usually around day 5 you can see something growing inside if it's fertile depending on how dark your eggs are. most people wait until day 10 before they decide if an egg is fertile or not. if there's nothing growing by day 10 there isn't going to be.
if at any point while incubating the blood veins vanish and there is a red shape (a blood ring) though it doesn't have to be circular. then that egg has died and needs to be removed to prevent contaminating the other eggs.
any eggs that give off a bad smell should also be removed. (all healthy eggs I've incubated smell as fresh as the first day they were put in.)
any eggs that have liquid coming out of them should be removed as soon as possible.
dirty eggs shouldn't be set, though I have set them myself. It's just more likely that those eggs could become contaminated.
air cell size should be monitored either by candling or by weight.
some eggs can have their aircell damaged, detached, or misshapen which could cause problems with hatching. these problems can be seen with candling.
all through incubation once you've seen movement, any eggs that no longer have a moving chick inside (usually accompanied with the blood veins disappearing and possibly a blood ring) are dead. if it's hard to see, so long as there is not an external pip you could "water candle" an egg. by putting it in a bowl of warm still water and seeing if there is any movement, that the egg makes on its own.
I don't know if I've covered everything. obviously doing as little to the eggs as possible is best, this is just stuff I've come across while learning how to incubate myself. this is in no way an incubation how to.
