Don't the torrent files contain all the hashes for each piece? Doesn't that mean if a single piece is bad, the entire torrent can't be verified? Torrent files contain a lot of useful data that isn't found in a magnet URI. Is this just being ignored?
The hash in a magnet URI is of the info dictionary in the .torrent file. It's used to query the BitTorrent DHT for peers running the same torrent. Once another peer is found, your client will download the full metadata file from it, and from there it works just like any other BitTorrent download.
