[dale_glass]

Not very anonymous unless you're really careful about it and never fail once. The localbitcoins person is linked to everyone they interacted with, and the transactions are public and timestamped. Unless you use a new address every time, your identity can be deduced fairly easily from your other activities.

The probable result is that the police nab the localbitcoins person, then pressure them to explain who they were doing business with, and go from there.

If anything it's worse than buying drugs in a dark alley because there's a permanent record of your activity.