Daren, there are likely errors in computing all these numbers, but they are probably a small fraction of the totals. Several things are going on as people learn more about the virus clinically.
Regarding the "asymptomatic" column on a table, what has happened is that in the beginning of all this the listed diagnostic symptoms were fever, cough, difficulty breathing, and in fact if you didn't have one of them you could not get tested. In the intervening months they have added a lot of other symptoms. For example odd ones like "covid toes"! Then they realized that some people might not complain of shortness of breath, but if they measured blood oxygen levels, they were really low. Then they discovered that some people get a clotting disorder from the covid, and clots form and wind up in the lungs, heart and brain, giving rise to heart attacks, pulmonary embolisms, and strokes. What this means is just because someone doesn't have one or more of the current list doesn't mean they are truly asymptomatic. I am willing to bet some nurse was filling out a multiple choice form where the last box is "none of the above" and it got counted as asymptomatic.
Skeets mentioned hospitals going back and reviewing causes of deaths in covid positive patients. This is a good thing, we could learn a lot from double checking.
As far as the asymptomatic people in nursing homes, at least so listed until they become dead, a bunch of things seem to be going on. The older you are the less vigorous your immune system. Some of the classical covid symptoms arise as a result of an immune response, and are subdued or nonexistent in the elderly. And then there is the possibility that no one noticed grandma wasn't looking too good.
As far as listing someone in hospice, as far as I am concerned, we are all going to die sooner or later, and if someone tests positive and dies suddenly, all we can do is assume covid hastened that death. Maybe by only a few days, but I see no other way of handling the data.
Re your questions on testing, short answer is the reliability depends on the particular test, and the people doing them. Pilot error is possible. As far as the test for an active infection is concerned it is highly specific for covid 19. A false positive could occur if someone somehow contaminated a swab, but the procedure is pretty foolproof. Easier to get false negative. There could be a sampling problem, e.g. is there virus in the part of nasal cavity that was scraped by the swab? Joke is if it doesn't feel like the tester was going for a brain biopsy it wasn't back far enough.
There are a lot of papers on this, I'll look around for more of them for you.
