There are several techniques to keep paper wasps from building inside nestboxes, or underneath them (e.g. Some work better than others, and some work better with native vs.
European paper wasps (The introduced European paper wasp is yellow and black like a yellow jacket, and become active in mid-June, with cells facing outward vs. It becomes "imprinted" on a nest site, so just destroying the nest doesn't work.) Native brown paper wasps are less aggressive and tend to build nests only on horizontal surfaces. Mites are uncommon in bluebird nests, but are common in Tree Swallows (TRES) nests.
Cowbirds usually toss one egg of the host clutch and lay their egg in its place.
Sometimes cowbirds will parasitize the same nest twice.
Boxes can also be paired (typically 5-20 feet apart.) **Mountain Bluebird and Western Bluebird ranges overlap in some areas, and Mountain's need a 1 9/16" hole. So the 1 9/16" hole is a safe bet, and will also exclude almost all starlings. A bluebird landlord should be prepared before opening the nestbox to check on a nesting, in order to deal with predators, parasites, wet nests, etc.
Nestboxes in areas with deciduous trees are usually preferred of chickadees, which also puts them at risk of House Wren attacks.
Adapted from the list posted by Chris (Gandi C) on the Nature.net/Garden Web Bluebirding Forum.
I am always verifying and adding to the information on this page.
House Sparrows (or HOSP) are deadly predators of bluebirds and other cavity nesters.
House Sparrows will peck eggs, nestlings, and adult bluebirds to death.