I have Transferred numerous Characters between Realms on NA Servers and have had zero issues until this last one that I paid for almost 40 hours ago. It's stuck "Queued" and is unplayable. Blizz's response is some bullshit about the Payment hasn't gone through, but I checked my Bank and sure enough it has. Then I tested their theory by purchasing a Token and low an behold, the Token purchase went through near instantly.
The only thing I've noticed is my Hearth tends to get reset to Org (Horde Characters) but that's about it.