It's hard to reference old messages. You have to wait until an archiving site picks up the message you want to link to, then look it up.
Assuming your listserv is working properly, this isn't an issue, since we're talking about old messages (referencing new messages might be problematic).
It's hard to reply to messages you haven't received from subscription, since you have to manually copy the sender and message contents.
If only someone would design a feature - perhaps even one integrated into the OS shell itself - for easily selecting and duplicating text. Perhaps it could be modeled after some increasingly-anachronistic real-world activity, like scrapbooking.
(I'm not actually sure what you're referring to here; continuing private threads in public tends to be a manual operation regardless of the software involved)
It's impossible to moderate threads of discussion. Posts cannot be deleted or modified without supernatural powers.
The reverse argument is that it's much harder for a rogue list owner to re-write history by deleting portions of the conversation that disagree with him, since one or more users will likely have their own copies.
It's tricky to keep threads together (namely, to ensure all participants in the conversation are copied/replied to).
Proper client software should handle this easily, as well as provide more flexible display and ordering of threads than most web-forum software allows.
It's tricky for users to participate in multiple high-volume mailing lists, as they have to subscribe and set up filters (or just be really involved).
High-volume forums are no easier. If anything, it's harder (if not impossible) to configure filters in web-forum packages. Either you're "really involved", or you're probably missing something.
What real edge do mailing lists have that didn't occur to me?
Privacy by default, without "yet another website account". Quick to set up. A natural progression from informal email chains as the group grows. No breaking context to move from email to web when processing replies. Familiar to almost everyone (yeah, yeah, Korean kids / the Facebook generation don't use email...)