Egg safety. When to eat and when to not eat

If the shell is undamaged, and the eggs are not past their expiration/best by date, they are safe to eat. Official source: your government's food safety agency, unless you live in a place with really really lax food regulation. But your profile says Australia - I'm sure things are fine there. If there are problems with salmonella outbreaks, it's not anything that you can detect. A salmonella-contaminated egg will look exactly like an uncontaminated one - that's why governments generally recommend you cook the egg, which will kill the salmonella and make it safe. If you're eating raw/undercooked eggs, you'll have to decide whether the risk where you are is low enough.

In practice, they're actually safe for a while after the best by date, just not as fresh, and if the shell is cracked without damaging the membrane or they were very recently cracked, they're also safe. But no damage and before the date is the most absolute guarantee you can get.

The two tests you mention will help you get some idea how fresh the eggs are. Neither has anything to do with good vs. rotten. As eggs get less fresh, they dry out a bit, forming a larger air pocket. So they'll slosh more, and start to float.

But it doesn't mean they're rotten. An actually rotten egg would be completely obvious by smell - they're sulfurous, a lot like the smell that's added to natural gas. If you're getting eggs that float in water on the day you buy them, with really obvious sloshing, yes, it means they're not fresh, so they're certainly not good as fresh eggs from a farm. So if that's the case, your supermarket isn't selling you good quality eggs. It doesn't mean they're unsafe, though.

As for "Why do most eggs have crap and blood on them?" ... "most" is a huge exaggeration, the places I've seen - they get washed. And as rumtscho pointed out in the comments, the eggs are coming out of a chicken, so some ugly stuff is natural. You never actually said what your eggs look like, but if you live in a place where they're not cleaned (even before selling in a supermarket??), then it still doesn't mean they're unsafe, just that you should probably clean them before cracking them.

And dark spots? Some eggs are naturally speckled - that'd be fine. If it's something else, I guess it would be helpful for you to provide a picture.

A floater does not indicate a rotten egg. It only indicates an old egg. When a chicken lays an egg there is no air inside. The shell is porous and over time water will evaporate out of the egg leaving an air pocket at one end. If you're concerned, crack the egg into a small bowl and smell it. If it smalls bad, discard. Cooking will kill salmonella, but no need to risk getting sick.

The USDA requires all eggs sold in the US be washed. This washes away a protective coating that keeps bacteria out of the egg. An effect of washing and removing the coating means you have to refrigerate the egg. Commercial egg producers coat their eggs with mineral oil to extend the life of the egg. Sailors will sometimes coat eggs with petroleum jelly to extend the life out to a year. In Europe, washing eggs is illegal. No washing means the eggs don't need to be refrigerated. Ironically the rate of salmonella poisoning due to bad eggs is lower in Europe than the US. Washing aside, salmonella can infect an egg from inside the chicken so sometimes the chicken is vaccinated against salmonella.

You shouldn't eat cracked eggs. The only exception might be that you know you cracked the egg accidentally on the way home from the market — but you would need to cook and eat it quickly.

It typically takes a few days to pack and ship an egg. Commercially sold eggs will actually have two dates on the carton. You're familiar with the best when used by date. There's also a "secret" date that tells you when the carton was packed. It's in Julian date format so you have to do a little deciphering. If the Julian date code says 365, the carton was packed on December 31. That gives you a better idea of how old the eggs are.