I'd like to know if it is possible to embed an image file inside a Scribus document.
If I try to do that with an image frame, it makes me select an external picture but apparently it doesn't really import it, it just link the external image.
This results in errors when I move the document file around.
How can I fully embed the picture?
No, you can't in the 1.4 stable version.
The development version 1.5.x (status April 2016) already has the feature you're looking for.
It's in the context menu (and also in the "item" menu, under "Image").
If you're using 1.4.x and you're goal is to transfer the .sla file to a different computer, then you can "File > Collect for output" your work and send the resulting directory (probably after having zipped it).
If you want to use on different computer a .sla file placed on a server (and it then has different paths), Scribus does no support yet this use case.