Somebody on the WoW forums wondered what the level 60 bosses were doing nowadays, and posted an hilarious fictious chat session between them, which is currently being copied all over the blogosphere. As the WoW forums are too temporary, I'm linking to it here and here. No need to copy & paste it another time to here.
[Spoiler warning - Read the chat at the links first!]
The chat is between the bosses of the level 60 instances and raid dungeons, who complain that they haven't seen any "mobs" (that is players) for days, until some mid-60s players arrive and do speed runs, soloing the bosses. Now I seriously doubt a level 64 warrior doing Molten Core solo in 2 minutes 34 seconds, but the sentiment is the same as in my Goodbye Molten Core post: Nobody takes the level 60 dungeons serious any more. Either they stand empty, or they are farmed in easy mode by higher-level characters. You can count the days until the first video of a handful of level 70 characters doing a Molten Core speed run appears on YouTube.
I haven't got a good feeling on how much stronger a level 70 will be than a level 60. I'm pretty sure that at level 64 you won't be able to solo even Stratholme or Scholomance, but will it be possible at level 70? I don't think a holy-spec'd priest is the good class to try that. If I ever get around to level my warrior to 70, with enough armor and magic resistance you should be able to do it. Molten Core won't be soloable at 70, but records will be set and broken with how few people you can do it. Just another occupation for bored level 70 characters with nothing better to do.