Can someone explain those free 0.00000001 BTCs? I've just noticed an odd transaction to my wallet address. 1LnNQDKV6DiMnZ2rZ9yXpcnnTh7my1WusP seems to be giving me a free 0.00000001 BTC.

Investigating further shows that I'm not the only one receiving the free 0.00000001 BTC. Take a look at the blockchain transaction.

What is happening? Is this guy using blockchain's public note as an advertisement spam?
You are right. This is a kind of advertisement which targets bitcoin users to spend bitcoin in a particular service. Something like an booklet which people in store are giving you when you have used their service.

But keep in mind that blockchain public note is not a function of bitcoin itself (by this I mean that you can not add it though bitcoin client). This is a service offered by blockchain.info and they just add this by attaching a field to their database. You can read more about it by reading their FAQ in the section public note.