Great info Efmesh, thanks
That shotgun brood pattern can be caused by matings with drones too closely related to the queen as described by Ef, and also occurs as one of the symptoms of Parasitic Mite Syndrome (PMS) via Varroa Sensitive Hygiene (VSH).
In bees expressing VSH, about 19-35% of capped larva containing varroa mites are cleaned out (killing mites and sometimes larva), leaving random open cells and a spotty brood pattern. So nowadays, the trick is to divine whether your shotgun pattern is from inbred matings, or PMS. With a shotgun or spotty brood pattern, some sort of mite count is in order. And then usually a mite treatment because poor matings are fairly uncommon. Keeping one to three hives between 1976 and 1992, I never did see a spotty brood pattern. It is not uncommon nowadays because of the prevalence of mites and the honey bee's effort to keep the mite population down using VSH.
I can see why your training focused on the haploid eggs and larvae because it is absolutely essential that you have a group of donor drones unrelated to the IIQ.
I'd be interested to hear from Chip, Iddee, Perry or other bee inspector the differential diagnosis between EFB and PMS. Don't mean to hijack your thread EF, please forgive me.