UPDATE: Bashiok posted that Blizzard will be "restarting some Garrison services" to address access and progression issues. He also says that Blizzard has implemented "dozens of hotfixes" over the last few hours.
UPDATE 2: For those experiencing long queue times, this is working as intended. Bashiok has said that Blizzard is reducing realm population caps in order to address latency. Rygarius has posted a list of hotfixes for November 13.
UPDATE 3: Lore tweeted about the issues: "So obviously launch not going as smoothly as we wanted. Will be many discussions in the near future about what could have been done better. Right now, however, we're focusing 100% on just fixing issues so everyone can play. Can worry about what went wrong later."
UPDATE 4: Lore says fixes have been implemented for garrisons, but he recommends walking to your garrison instead of flying there or using a hearthstone.
Despite a mostly smooth launch so far, some realms are now experiencing major problems as more and more players crowd the servers. Garrisons on Argent Dawn, Cenarion Circle, Khadgar, and other realms are currently bugged and not always phasing properly. Twitter user @ikolism posted the image above of players in an unphased Horde garrison. Normally you're only supposed to see the players you've invited to your version of the fortress...
Players can become stuck inside their garrisons, or stuck outside and unable to "zone in." If the entire garrison server crashes when players are inside it, they are reportedly sent back to where their hearthstones are set. For many that means an unexpected trip back to Orgrimmar, Stormwind, or Pandaria.
High population realms, particularly in the EU, have experienced world server lag and crashes.
CM Lore tweeted an update on the problems, but did not provide an ETA:
Still working on server and garrison issues. Making some headway, exploring as many options as we can find.- Lore (@CM_Lore) November 13, 2014