The USDA, generally on the very safe but a bit paranoid end of the spectrum, says:
After eggs are refrigerated, they need to stay that way. A cold egg left out at room temperature can sweat, facilitating the movement of bacteria into the egg and increasing the growth of bacteria. Refrigerated eggs should not be left out more than 2 hours.
(They also say some very sad things about Easter egg hunts.)
So if you're being strict, three days would be way too long. In reality, you'd probably be okay. The chances of getting salmonella are definitely higher, but are presumably still small (though I can't say exactly how small, of course). Personally, given the price of a dozen eggs, I'd probably play it safe.
Another answer mentions that in the UK eggs are stored at room temperature. That's true in quite a lot of places, but I'm guessing that they've avoided the large temperature swing issue mentioned by the FDA, so if your friend's eggs were refrigerated in the store, the situation's not quite the same as in the UK.
I have heard it stated before, but here it is from various sources:
Source 1
Source 2 (confirms the shake test)
Source 3
In general, the air pocket in an egg gets bigger as it gets older due to the permeability of the shell. I think the shake test is a little hinky, unless it actually sounds like water sloshing. I would try the float test; fill a bowl to twice the height of the egg, and place it in. If it sinks to its side, it's fresh. If it stands on its end, it's probably good, but needs to be used quickly. If it floats, toss it.
Best Answer
Would you risk getting sick for ~ $4. It's not like you left a tin of Beluga caviar in the trunk for 3 days. Toss them!