What trust am I placing where when I use Electrum?
"We" are volunteers running Electrum servers. There's almost no trust in them, the absolute worst they can do is feed you false negatives about the balance of your wallet, or they can also choose not to broadcast your transactions and pretend that they have. You trade some privacy in that they can see the contents of your entire wallet and associate it with your IP address. The client supports Tor connections if this is an issue for you. 

The blockchain is 22Gb now, actually.