There are many ways to promote good statistical practice. For example, one-on-one tutoring by experts would likely be invaluable to those receiving the tutoring, if a somewhat inefficient use of expert time. We may not be able to pursue every form of encouraging good practice within the goals of the SE network. CV's central purpose is a statistical question-and-answer site, so we need to keep that in mind.
Within that central purpose, I see two obvious ways to have some form of tutorial using the features of SE that are already available:
The blog. While the blog hasn't updated in a long time, several of the blog posts have elements of tutorial in them.
Tutorial posts aren't explicitly listed on the about page, I think it wouldn't take much to convince people to add it - currently the blog isn't being used at all, so why not?
An explanation about the blog and how you get to post to the blog is here. You might have to get the mods to revive the chat mentioned there.
Questions and answers. If you see a burning need for a tutorial, you can frame it in the form of a question and answer (it's completely legitimate to answer your own questions).
Such a situation came up for me a while ago, when in the course of answering a question I needed to use interpolation, and realized the OP wouldn't know how to do that. (I'd previously answered several other questions with the same problem -- but to explain interpolation in a post which was primarily about something else would be getting too far off track.)
So I decided to put up a tutorial on interpolation in tables in the form of a question and answer - one that I (or anyone else) could link to whenever needed, rather than giving an overly-brief half-baked explanation every time or pointers to less directly relevant material off site.
There are a few such questions-with-answers written by other people on the site (and I think we could stand to have more).
[If you're looking for tutorials with broader participation on a single good answer rather than a potential plethora of answers, you might even seek to set up some community wiki questions for the purpose.]
Shorter tutorials would be well placed for Q&A, longer tutorials would perhaps be better as blog posts. (But the 'post of the week' option on the blog allows for highlighting of questions/answers on the blog as well.)
If you do either of those things (organize blog post-tutorials or Q&A tutorials), or manage to get others to do some (I'd love to see a few tutorials from some of the experts), I would be cheering.
Indeed, if there's a topic that there's an obvious need for a tutorial on, I could perhaps contribute one, or contribute to one, as long as it's something I know a little about.