Hi Andre,
I am pretty sure any changes in 2.0.3 did not make it worse in this regard (i.e. the problem in the listed bug, and any similar problems, were in original 2.0 as well).
The file download issue is a slightly different one to the one mentioned. The other one was about viewing pages. With file downloads, depending on settings you may not even go to a separate page which may mean it is unable (using the normal mechanism) to update completion tickboxes on the page that the user is looking at.
You may be able to minimise this problem if you set the file option that means it opens a new page in the browser instead of downloading immediately. That way at least once students return to the course page, the extra options will be there.
If this problem does occur as expected, please file it (complete with minimal steps as to how to set up a new course to reproduce it) as a new bug using the Moodle Tracker. (In general when there is a problem and it maybe relates to a bug that was already fixed - you should file a new bug and not add to or reopen the old one.) You might also want to add a comment to the old bug, giving the number of your new bug, since it is a related problem and that might help people locate the new bug.
I am not sure exactly how to fix it but it should probably be possible (most likely by adding some javascript that causes it to reload the page after downloading the file) so if you file a bug I'll take a look.
--sam