Is it necessary to check hard or soft boiled eggs for blood spots?
I've never seen anyone do it, so perhaps it is not, but if so, why?
When the Lubavitcher Rebbe would eat the Beitza by the Seder, he would not check it for blood. Otzar Minhagei Chabad quotes the Taamei Hamitzvos who says that the AriZal would eat fried eggs and was not concerned for the occasional blood spot.
The Eishel Avraham (Buczacz) writes that because a majority of eggs have no blood-spots and it's hard to check them, one doesn't have to be machmir and find other food to eat.
In answer to your question, according to this article from OU, no:
There is no problem with eating eggs cooked in the shell (boiled or roasted), even though these cannot be checked.
However, note that this would only apply to non-fertilized eggs (as are commonly available today). If you're dealing with fertile eggs (usually available at a premium), consult a Rabbi for guidelines.
I also saw here that even fertilized hard-boiled eggs would not need checking. Only soft-boiled ever needed checking (when fertilized).
Also interesting from here:
When eating hard boiled eggs, Harav Moshe Feinstein zt"l had the custom to peel back the white to check the surface of the yolk for blood spots, which would appear as black spots.
You don't have to. In fact, it is impossible to do so since after cooking, the blood can get mixed up and not be noticeable. Since it is impossible to check, we rely on the rov (majority) or eggs that are not bloody.
From Halachically Speaking Volume 4 Issue 18, "Blood Spots In Eggs":
When eating hard boiled eggs, Harav Moshe Feinstein zt”l had the custom to peel back the white to check the surface of the yolk for blood spots, which would appear as black spots. [ This is not required (This is the opinion of Harav Yisroel Belsky Shlita (Hakhel Janurary 2006 daily e-mail).]
As mentioned before, according to the Rama, before using eggs in food, one should check to see if there are any blood spots. However, if it was not done, it is permitted to eat a hard boiled egg which was not checked beforehand since we can rely on the fact that most eggs are not fertilized
See there for sources.