your post makes me ask both of you who are having trouble if you are using a slow dial connection or broadband. what you describe sounds like it could be the connection itself rather than yahoo's servers.
tommywho70x has been my member name at yahoo for most of the past decade and i've never had significant problems with their servers. i have had trouble like you describe over a dial-in connection.
I've been using Yahoo Mail since they first launched the service - which must have been in the mid 90s.
The problem was a server upgrade. I did a search and found that others have been getting the same error message as Yahoo has upgraded servers around the world.
Here's what chaps my hide: why didn't they announce it to users? I wasted a bunch of time trying to diagnose problems on my home systems and network, and was worried that someone had hacked into my account. (This was before I actually got to the point of receiving a proper error message).
If I didn't have hundreds of contacts that use that address for some of my professional activities, I'd have switched to something else. The big issue is: what service? I refuse to use anything associated with Google, and have not had good experience with AOL or MSN services.