Could micrograms of polonium really change the viscosity of a whole teapot? I was reading How radioactive poison became the assassin’s weapon of choice and it opens describing how


  The men eventually left, and Andrade cleared the table. As he poured the remaining tea away, he noticed that the consistency of the liquid that tipped into the sink was strange. Gooey. He couldn’t have known it as he puzzled over its weird yellow tinge, but the man who’d been sipping the tea was a 43-year-old Russian dissident called Alexander Litvinenko, and the tea itself, draining away into the London sewers, was lethally radioactive.


Later in the article it mentions the total amount he ingested was about a microgram. 

Now, skipping past the part on how you wouldn't notice you are drinking gooey tea, could micrograms of polonium change the viscosity of a whole tea kettle?

It doesn't say how much he drunk, or the size of the teapot, so lets take some guesses. Lets assume he drank a very small amount of tea, say 10 mL to give us a decent upper bound on the concentration of the solution. So that would be 0.1 micrograms/mL or about 0.5 micromolar. 

Could a solution in this concentration range change the viscosity of water enough for a casual observer to notice?
I think it is highly unlikely polonium makes water notably more viscous. The concentration is just too low, and radiation doesn't make water more viscous, controlrods are cooled using water and they produce a lot more radiation.

what can happen in the case of tea is that the radiation induces the formation of free radicals that in turn initiate polymerization or other reactions that form larger molecules which would make the solution more viscous, this still sounds highly improbable though.

there are multiple studies on radiation initiated polymerisation:
http://large.stanford.edu/courses/2012/ph241/weil1/