I always crack eggs into a saucer before doing anything else with them.
Even if they're not the freshest, if they smell OK then to me they're fine.
I use my nose, and rarely have to throw anything out. It really grieves me to have to throw anything out, so I make a lot of what my mother used to call 'dustbin' soups - mostly fresh veg, pearl barley, etc., but also including that one dried up rasher of bacon or bit of ham, leftover mash or boiled spuds, any limp old carrot or bit of celery, a few sprouts or a leek that are past their best but OK once you've peeled the top layer off.
With fresh meat, your nose will soon tell you if it's gone off.
When clearing the flat of dh's old aunt after she died, we found several tins of veg and soup, etc. - some of them years out of date.
But since the tins were all perfectly sound I took them home and we used them all.
We're still here!