Either it has already been fixed, or else I recommend coming there when there's less people, compared to first evening of the game. I was able to finish it without trouble early in the morning.
I don't think it was ever broken on launch. It's just that there is always a massive crowd trying to finish it at the same time. Come back when everybody gets tired of waiting - worked for me at least.
I'm also having the frog race bug. Not able to complete after choosing bloodthirster, feeding him, then putting him at the start point. Nothing happens after that.
I experienced this bug last night. It appears that relogging will frequently put you into different server instances, and in some of those instances, the quest may actually be working. I was able to get around this and several other "Event quest" bugs by relogging last night. I think it took about 5 attempts to get into an instance where the In Name of the Queen was working.
I was unable to finish this quest not only yesterday but in the last two betas as well. Tried everything suggested. But, I glanced at the forums breifly last night before going to bed and read some folks were able to finish it when nobody was there. Couldn't resist so I got back on and ran over there and sure enough I was able to finish the quest. There were only 2 other people there.
Having to wait and find a time when there are fewer people in a quest area is not a long term solution but for now it does tend to work.
Great advise, Evergnar! I agree on it being a poor long term solution, but it's nice to know there are work arounds to most/all of the currently bugged "event quests."