You can remove meat spots, either before or after cooking. Blood spots, if they're not bad, I usually ignore.I had no idea you can eat bloody eggs, what about if it has meat spots?
Some hens are prone to laying eggs with meat or blood spots, so if you can ID which hen/eggs those are, those are the ones I pull aside and don't use for hard boiling (since you can't open it up to remove the spots, and I don't want to serve eggs with spots inside). They're fine for baking with, scrambling, etc. as no one will see the spots once you remove them.
If meat/blood spots gross you out, it's best to crack each egg into a cup for inspection before mixing into a batter or putting into a hot pan, so you can remove any spots before cooking.