> unix wizards will tell me a better way of doing this

Great story. I won't claim to be a wizard, but here's mine:

    grep -Eo "mailto:[^\"']*" webpage.html | sed 's/^mailto://' | sort -u

The pattern means "mailto: and then everything up to a single or double quote", and the -o flag means "only show the matches". The main benefit of this approach is that it works even if you have multiple email addresses on a line.