In their haste to reproduce, they don't take time to rebuild nests between broods, like most birds do. Often, fecal pellets from young pigeons accumulate, and help cement the nest together. Unhatched eggs and even bodies of dead nestlings are sometimes incorporated into a nest.
WHAT'S THE MAJOR CAUSE OF BIRD DEATHS? If you said "cats" guess again. By far the most drastic declines in numbers of birds stems from habitat destruction via human activity. Some call it "development", and much of its impact is unplanned or poorly thought through. The second cause of death is birds crashing into man-made objects such as windows, power lines and wind turbines. Cats (especially feral) are certainly guilty of something (hunting is in their nature after all) but aren't even close to the top of this list.