I'm trying to use AllVideos in Joomla 3 in a module, but all I get is the code text displaying. If I move it to an article, it then works - but I thought it's supposed to also work in a module... I do have load content modules enabled already. What else could be wrong?

I'm having the same problem with a 2.5.20 site. Current version of allvideos, working on another site with same versions and same videos.
An example of it working in an article but not in a module is here on a prototype site:

bit.ly/1hXQaVL

I was able to get this problem fixed by going under the Module > Options - then setting "Prepare Content" to YES. Hope this works for you too!

@Jacki

Yes this the solution. AllVideos is a content plugin so any extension using it should be able to parse content plugins.