Can someone please explain a security aspect of BitCoin to me?

[Crystallas]

It's all on the blockchain.

The blockchain is anonymous. It shows transactions but no way of telling who owns the addresses

Yep, which IMO, is a major... MAJOR plus for security. Like others have said, if you want some type of extra verification service, they exist as well.

[mithrandi]

The transaction is of course visible in the blockchain for anyone to see, and since you control the sending address, you could sign a message using the key(s) of the wallet address(es) the payment was made from if you needed to prove that you are the person that sent the transaction. Unfortunately, there is nothing stopping the *recipient* from claiming that the bitcoin address you sent the funds to is the wrong address; I believe this is something that the "Signed URIs" proposal at http://electrum.org/bitcoin_URIs.html is attempting to solve, but I don't know if any online store currently implements this.

[Aztec]

Yep, which IMO, is a major... MAJOR plus for security.

Completely agree with this. I don't want every tom dick and norbert knowing what I'm buying on Silk Road

[flavius]

A transfer being reversible is just as bad as it not being reversible. You can't win when it comes to selling online, either the seller takes a loss, or the buyer does, there is no middleground that fixes everything.

If it's reversible sellers will lose money, and you have to realize it being reversible would be pointless if the user had already moved the money, since you can't have a negative bitcoin balance.