Hi there, I just saw this & thought I'd add a some insights that I think may be helpful.
I have been keeping both free-range & cooped chickens for a few yrs, so I often find eggs that I'm not sure of when they were layed. I've found that eggs can sometimes last a lot longer than we'd think, (and that store-bought eggs are a lot older than I'd previously thought!) I collect eggs both for eating & for incubating & I don't like to waste any eggs, so I've developed a system for determining what I do with each egg & it has worked perfectly for me so far. I inspect each egg for freshness & quality using a combo of visual inspection, a float test & candling. Then I grade them from 1 to 4 (1 being the freshest, 4 being unusable). My family (and anyone we give eggs to) gets only #1's- the freshest ones to eat. #2 eggs are just a bit older. The air cells will be bigger, but still good & safe to eat. #2's can also be #1's that have been in the fridge too long, or newer eggs that have cracks in the shell or loose air sacks, or anything else that may make them spoil quicker/ or make them unappealing as people-eggs. #2's either get boiled for animal feed (extra protein), or go into the incubator if suitable. #3's are usually not suitable for people to eat, but ok for animals. They're usually old eggs that have large air cells & fail the float test, but have not gone bad yet. Also, eggs that have spots on the yolks but are not rotten. 3's get fed to animals, or chucked if I am unsure at all if they are safe. #4's are spoiled eggs, partially incubated eggs, or very old eggs with air cells (larger than 1/3 the size of the egg), or old eggs with thin, pale, runny yolks. All #4's get thrown out.
Candle your eggs 1st: not only will that tell you immediately if the egg is rotten or has started to grow, but will also show any fine cracks in the shell. With practice, you will also be able to tell the age (& freshness) of the egg by the size of the air sack, which gets larger as the egg ages. Candling can easily be done by shining a small flashlight into the egg. I've found it is easiest to see into the egg in a darker room. Make a seal by making a tight circle with your hand around the end of the flashlight, to block any light except for a small beam coming thru your fist. Then hold the fat end of the egg against your hand, up to that beam. You should see the air sack on the fat end. On a fresh egg it is small- usually smaller than a dime. It should stay in place & no edges of it should move if you turn the egg. The rest of the egg should be clear & the yolk (if visible) should be round-ish & slightly firm, & will roll around a bit when you turn the egg back & forth.
If the inside is not clear or there are any dark patches inside the egg (besides the yolk), throw it out. If the yolk has an easily seen spot in it, that is much darker than the yolk & bigger than 1/4 of an inch or so, it has most likely started growing. I either try to incubate those, or throw out. Those can still be safe to eat (can be animal feed when cooked), but I prefer to not cook b/c they'll have a blood spot in them when cracked & I'd rather not deal with that.
If the air sac moves around (think the bubble in a level), it is dislodged. Those may still be ok to eat, but a failed air sack will cause an egg to spoil more rapidly, (just like a crack in the shell will), so only eat if you know it's fresh & it passes a float test. (I cook these up for the animals). Any egg with a displaced air sack that has any discolored spot in it is most likely rotten & should be thrown out.
If you have many eggs to check, a float test is a good idea to check age, as older eggs have larger air sacks, so will float more. However, even if an egg is more buoyant, it can still be safe to eat (or cooked & fed to animals). In this case, candling any "floaters" is a good way to determine if they are still edible, or too far gone. As an egg ages, the yolk will break down & become much more liquidy (less viscous). When candled, these yolks will look pale & flattened compared to a fresh egg, and the inside of the egg will look more watery. Once they get like this, they are very close to spoiling, so I throw those out to be safe. Hope all this is helpful, but please remember that if you are in doubt to always err on the side of caution & throw out anything you're not sure about!
I bet it’s like eating mud. 
