On Graphic Design we currently have some handy tag-specific alerts when asking questions with certain tags. These are for certain problem questions that are only a good fit for the site if they follow certain requirements. The alerts list these guidelines and specific requirements.
These are also implemented on many other sites. They were requested on Science Fiction & Fantasy but apparently never implemented, leaving them to come up with alternatives. As far as I'm aware this is something that a developer needs to put in place on a case by case basis and isn't currently possible for mods to implement.
We plan to test a new, 'guided' version of the ask question page soon. This page would essentially break down all of the elements that make a great question, and give the user plenty of guidance as to why it's to their advantage to understand what's needed in each of them, and provide it.
Now, I don't know what this new 'guided' version of the ask question page is or what it looks like, but this should be a part of it. Tag specific requirements are an important part of asking competent and useful questions and these requirements are not obvious to new (or existing for that matter) users.
The notice needs to be static, more prominent, and permanent. (I'd argue against removing the notice at a certain rep/privilege threshold. Maybe remove the notice for users with a certain tag specific badge for the tag in question.)
The ability to add requirements that need user interaction to comply with. This could be as simple as a check-box, but there needs to be a distinction between dismissing the notice (which is what you currently do) and acknowledging, complying or agreeing with the notice.
This needs to be possible to implement by non-developer users. Probably only moderators, but possibly at a certain privilege (maybe Trusted User, along with tag wiki edits).
Show the notice as soon as the tag is added. Currently the notice only appears once the user moves focus away from the tag input field, this means someone can write a post, tag, then hit "Post Your Question" without ever seeing the notice.
A quick mockup
I'm not totally sold on my mockup, it's just a quick idea. Maybe the check boxes on each point are too much, I don't know—but there needs to be some interaction. Also note the lack of a dismiss button.
As for arguments that this makes it harder for new users to ask questions, I would argue that asking bad questions that are then closed because they didn't follow some obscure rules they weren't aware of is worse for user experience than the added (slight) extra hurdle to asking a good question to begin with.
All in all I think this will give everyone a better experience. New users know what is expected of them up front and don't have to deal with the frustration of questions being closed and complaints in comments and regular users don't have to deal with the constant stream of badly formatted questions that hover between being on and off-topic.