The Wikipedia article Cause of Yasser Arafat’s death quotes a report claiming,
an unexplained quantity of Polonium-210 has been detected on the personal effects of Mr. Arafat.
Seems they’re not looking at decay products at all. The tests are claimed to have been done almost 20 half-lives of ²¹⁰Po after Arafat’s death; how much of a 1µg lethal dose would be detectable? (2⁻²⁰ ≈ 10⁻⁶, or one part in a million; do you believe a test that claims to have found a picogram of the stuff?)
As far as decay products, http://www.nlm.nih.gov/medlineplus/ency/article/003360.htm suggests normal levels are “less than 20 µg/dL of lead in the blood”. Assuming 5L = 50dL of blood in the body, and ignoring the rest of the body, 1µg of ²¹⁰Po would yield an excess of—at most—2% ²⁰⁶Pb. There’s no plausible way that was detected, given the variation in the percentage of ²⁰⁶Pb in normal lead.
