Taking on a new protein source, like pigeons, is attractive but you want to consider what input you will have to devote versus what output you are going to get. Consider the time and money you will have to invest, constantly, versus the likely meat meals. Consider just trapping an occasional bird or raiding their nests for squab when you feel like it, and otherwise letting the birds "free range."

Can I have your share of both?
-Blast, eater of many different things...

You should always cook grasshoppers as they may have tape worms, right? Or am I thinking of another bug? Is it safe to say you should cook most bugs before eating?

Insects are intermediary hosts for a number parasites including tapeworm. For example grain beetles are an intermediary host for a type of rodent tapeworm. Although humans may not be the definitive host for these parasites, humans (aberrant host) can and do occasionally become infected by these parasites. I would cook all insects prior to consumption.

Pete

I cook everything except fresh fruit, berries and a few of the vegetables
Some of the fish from certain salt waters are safe to eat raw but I usually still cook them.

I agree, most likely it is rare occurrence to become infected with a parasite by eating a raw insect, all it takes is one time. While most of these references examine the life cycle through non-humans, keep in mind that usually humans are not considered primary consumers of these insect intermediaries. Human can act as aberrant hosts and in some cases the effects can be even more devastating than normal hosts. While I did not enough time to run a full search, here are a few references.

Pete

From Link 1

Eating the intermediate host. In other cases, the principal host may ingest the intermediate host harboring the infective stage. This is true of the lungworm Metastrongylus, whose infective larvae are ingested in their earthworm intermediate hosts by pigs.
Acanthocephalans
Eggs are discharged into the body cavity of the female worm, where they develop into larvae surrounded by a shell of several layers. The embryo, known as an acanthor, has a spiny body and an anterior circle of hooks. The ancanthor inside its thick-walled egg is resistant to the environment and can live for years outside the pig. However, it will develop only if eaten by a dung beetle grub. Pigs become infected by ingesting the grub or adult beetle containing the encysted worm larva.

From: Link 2

Remarkably, an indirect, two-host cycle may also occur, involving grain beetles, fleas, or other insects that feed on contaminated rodent droppings. Insects that ingest the H nana eggs can serve as hosts for the cysticercoid larvae. Humans who accidentally ingest infected grain beetles (some of which, such as Tribolium, are only 2 to 3 mm long) digest the cysticercoid free; digestive enzymes then act on the cysticercoid to release the scolex, which attaches and develops by this indirect cycle into an adult worm identical to that acquired by the direct life cycle.

From: Link 3

Tapeworm eggs pass through the feces of these animals and fleas and lice ingest the eggs and act as vectors to carry intermediate stages of the tapeworm. Dogs or cats may accidentally ingest the insects and the intermediate stage of the tapeworm can grow into an adult.

From: Link 4

Eggs of Hymenolepis nana are immediately infective when passed with the stool and cannot survive more than 10 days in the external environment . When eggs are ingested by an arthropod intermediate host (various species of beetles and fleas may serve as intermediate hosts), they develop into cysticercoids, which can infect humans or rodents upon ingestion.

The problem is many of the diseases that were traditionally confined to areas of the world with less than ideal sanitary conditions are working their way into many areas that have long been considered insulated from endemic and epidemic conditions.

Pete