I am getting the same error with the demo:
http://demo1.b2evolution.net/stable/

Should be moved to bug reports.

How do I reproduce this?
I just uploaded a file on the demo without a problem.

Sorry, was not clear that the error comes when trying to Add/link files, not just upload.

Steps to reproduce:

1. Go to http://demo.b2evolution.net/ and autologin.
2. Click New post
3. Give the post a title and a text.
4. Click Add/link files and the post will be saved.
5. Now clicking on Add/link files won't do nothing.
6. Go to posts list and open the post again.
7. Now click on Add/link files.

Error:
Fatal error: Call to a member function get_next() on a non-object in /home/demo1b5/public_html/stable/inc/files/files.ctrl.php on line 201

URL: http://demo1.b2evolution.net/stable/admin.php?ctrl=files&mode=upload&iframe_name=attach_v6aRibieT0vKecft&fm_mode=link_item&item_ID=32

You can also try to link files on this post:
http://demo1.b2evolution.net/stable/admin.php?ctrl=items&action=edit&p=32&redirect_to=%2Fstable%2Fadmin.php%3Fblog%3D1%26ctrl%3Ditems%26p%3D32%23item_32

Doesn't work for me.

ok, got it. thanks. We're gonna fix that.

Already fixed http://forums.b2evolution.net/viewtopic.php?p=107926#107926

Yes, your fix will be included in version 4.0.5.

Thanks :)

Thanks a million, Sam! Your help is much appreciated for a quick fix!