After decades of blood donation I was rejected in 2010 because of a false positive HTLV I/II test.
I was annoyed, but not too concerned. I forgot about it until I came across old papers today, and a Google search showed that this has been a problem for others. So I'll explain here what I know of this topic, and why I wasn't worried.
This is a bit hard to explain -- even physicians have trouble with testing concepts. One way is by a simplified analogy made for this situation. Suppose you were looking for a killer and you knew they blue eyes and a unique DNA marker that's expensive to test for. Blue eyes would be your imperfect screening test; it has lousy accuracy but it's cheap. Next you test the blue eyed people with the expensive (and perfect) DNA test and you find your killer.
You could test everyone with the perfect "DNA Marker" test, but that would cost a lot of money. So the "blue eye" test is used first to save money.
In my case I tested positive on the cheap ("blue eye) screening test but negative on the good (but expensive) test.
So you'd think I could still donate blood -- but one problem is I may continue to test positive on the inaccurate screening test. That means each time I give blood the expensive test would have to be repeated. That's too much money to spend since we have enough blood donors. (We use far less blood that we used to.)
There are other procedural workarounds, but they all introduce cost and complexity. On the other hand, I'm still a listed bone marrow donor; in that case the economics justify the expensive test.
There's a reasonable discussion in Transfusion 2011 - Human T-lymphotropic virus antibody screening of... [Transfusion. 2011] - PubMed - NCBI. There were 130,000 false positive US donors between 1995 and 2008.
There's a better screening test on the market now so this problem should become less common. Blood centers may eventually decide to reinstate people previously rejected for HTLV positivity and rescreen, but that's probably more trouble than its worth.
If you think about this a bit, there are some other issues to consider. I wasn't much bothered by my false positive test because I'm a physician who works with these topics -- but I bet most of those 130,000 people were quite anxious. Money was spent on follow-up visits with expensive specialists and unnecessary retesting. Some may have had insurance problems. Arguably blood donors should be warned about the risks of false positive testing prior to donation -- so they have informed consent prior to the procedure.
Update 11/26/2015: It helps to have some long term followup on these strange happenings. In retrospect this might have been an early indicator of an auto-immune disorder. Two years later, in 2012, I developed acute inflammation of a distal (near nail) joint of one hand. Five years later (2015) it involved 3 joints and I have sub-patellar arthritis on both knees. In addition to an inflammatory arthritis along the psoriatic-osteoarthritic spectrum I've features of metabolic syndrome despite a low BMI -- including slowly elevating glucose.
My (newly acquired) rheumatologist and I suspect this was a sign I was pumping out lots of antibodies, part of a dysfunctional immune system activation. Though there has also been a relationship between HLTL-1 infection and polyarthritis that doesn't seem to resemble mine, and of course the follow-up testing showed I didn't have the infection.
If someone has a false-positive HTLV-1/II test when donating blood it obviously doesn't mean they are in the early stages of an auto-immune disorder. This is just one odd case. Still, it might be worth a retrospective study.