Re: Isn't that factually incorrect as well?
Transactions are relayed across the network in a matter of seconds. Each node in the network checks the transaction for validity, including if the sender had enough funds to spend. They do this by looking at their own copy of the Block Chain to see what the balance was in the sender's account(s).
For buying a beer, this level of verification is sufficient - the bartender doesn't have to wait. Bitcoin "miners" take incoming transactions, like any other node, but also attempt to find special hashes (checksums) for a set of transactions. That's called a block. The block also includes the previous block's hash as data. If anyone tries to alter the contents of a block, it no longer will match it's hash. If more blocks have been produced since, you would not only have to find a matching hash for your altered block, but every one after it, because each hash is part of the data for the next block.
By design, the special hashes are so hard to find, that the entire network of miners takes 10 minutes on average to find one. Since they are all busy making new blocks to claim the block reward (worth $15,000 per block at the moment), there isn't enough computation power to generate falsified block data.
So, you can see transactions validated to a reasonable level arrive in seconds. But over time the accumulation of blocks makes the record of that transaction effectively immutable. The bigger and more important the transaction, the longer you might want to wait for more blocks (confirmations) to arrive. Six blocks (one hour) is considered good enough to buy a house with. Conversely, if you are selling a house, you might want to wait for 6 confirmations on the buyer's funds, to make sure his money is good before the purchase.
> I also thought the block chain of a given coin can be analysed to discover the history of every wallet it's ever been in.
The Block Chain is a public record of every bitcoin transaction, ever, from the creation of a given coin in a particular block, and where it's gone afterwards. But the transaction records only the amounts, and the addresses it come from and goes to. A wallet can hold multiple addresses, and most of them generate new addresses for new transactions. Wallets are just files that hold the private keys tied to an address, which allows you to sign transactions for the balance held in that address. One file can hold a lot of keys, they are only 32 bytes long each.
Which wallet controls a given address, and who owns the wallet and where the file is located is not part of the transaction, thus it cannot be deduced from the Block Chain itself. It has to be found from other data elsewhere. If I spend bitcoins with an online merchant, and give them a delivery address and name, then they know who I am. But since bitcoin addresses are not typically reused, them having my sending address is not useful, it's been emptied. I'll automatically generate a new one for the next transaction. That's much more secure than with bank credit cards, where the number stays fixed for the life of the card.