And, for the record, the Auction House works well for me. Each action generally takes a second or two to complete max, even at peak times.
Which AH?
Thing is, if you spend a large part of your time in Kalimdor you're unlikely to see any problems. Mail and AH are responsive, no lag, no client freezes, no boat drops, no problems at all.
Eastern Kingdoms, however, are pretty well screwed. Particularly Iron Forge. Most evenings you can forget using mail or AH -- they simply do not come back with data. Ever. If it's particularly bad forget using the boat unless you like using a Spirit Healer. And don't zone (no NPCs will show up) or die (corpse won't show up on minimap, when you get in range you won't get a dialog box, when it eventually does popup it will take 2-10 minutes to rez).
And all of these problems are outside of the login server issues -- where the login server simply doesn't work for a lot of people from starting around 7:30 EST for an hour or two. Several nights it's been so bad that Blizzard couldn't get the login server back up for 6+ hours and credited
everyone 24 hours of playtime.
Maybe you're not having these problems. I'd be surprised. And the fact that Blizzard is crediting accounts indicates that it's hardly a minority of people having problems like this. The fact that Blizzard has taken down most servers for effectively the entire day indicates that as well.
Of course, Garona is one of the few non-PvP servers that hasn't been taken down. So that may be why you're not seeing them -- Garona is either running on beefier hardware or has a lower populace than the other servers. I won't presume to know which.
Are these issues (excepting the login server one) game stopping? Not usually. The inability to use mail or AH is really freaking annoying though, and the nights where lag is really bad it does render the game unplayable (the worst was the night when my instacast spells were taking 10 seconds to cast. No, I'm not exagerating -- this was in Menethil Harbor too, not IF). But they definitely take off some of the shine of the game -- it's just a good thing that WoW has so much polish on it in general.