Basic science question: if the polonium remained on his toothbrush etc. - why would it have decayed in his body?
Nor do isotopes help with much shorter half lives, as they're gone before you have the time to administer it.The question is phrased in a way which suggest to me that you make some unjustified assumptions. All Polonium decays*. It is a radioactive element with a half life of about 138 days. This means that every 138 days, half of the polonium have decayed. If not planted, the Polonium on the toothbrush is what remains from a much larger quantity of Polonium which has not decayed. (By a factor of a million, more or less.) That is why there are claims that the test results showed too much Polonium.
* To be pedantic, we are discussing The Po 210 isotope. But the whole point of killing with polonium is its fast decay, which results in radiation poisoning. You wont get much radiation poisoning from material with much lager lifetimes.
Nor do isotopes help with much shorter half lives, as they're gone before you have the time to administer it.
There is a difference, though, between Po-210 half lives in and outside the body. Outside the body, it is only subject to the physical decay with 138 day half life. Inside the body, there are also biological processes at work that try to get rid of the polonium, thus giving a combined half life of around 50 days (CDC source). Of course, those processes stop at death. But it means that if (big if) polonium traces are found in Arafat's body, it is very very hard to determine how much polonium he had been administered in the first place.
Why would it be assumed that it was Israelis who would assassinate Arafat?
We haven't even cleared the first hurdle to establish that he was assassinated at all, by anyone.
It is impossible to tell what they were cheering for. Real my ass.I had to laugh -- just after 9/11, when there were that day films of Palestinians cheering the towers falling, apologists claimed, fake! That's old footage of something else! CNN was like, "Like hell it is!" and it turned out to be real.
On topic: as has been mentioned, polonium 210 has a way too short half life for those people to have found anything after that long. And to those referring to Litvinenko, I wouldn't be so sure it was polonium 210 that killed him either.

I've had plenty of lager in my lifetime, but do you really think Yassir was a victim of alcohol poisoning?* To be pedantic, we are discussing The Po 210 isotope. But the whole point of killing with polonium is its fast decay, which results in radiation poisoning. You wont get much radiation poisoning from material with much lager lifetimes.