I have a client who has a Joomla 2.5.8 site running K2. It totally refuses to take the upgrade to Joomla 3.anything. In the end I gave up, did a brand new install then migrated over menus, and K2 items, categories and users by doing a MySQL export/import.

Whilst everything came over OK, I have 2 issues. I'm getting the errors:

Warning
JUser: :_load: Unable to load user with ID: 42
JUser: :_load: Unable to load user with ID: 117
JUser: :_load: Unable to load user with ID: 116

These ARE (not were - they still exist) users that I imported. Problem 1.

Second problem is a lack of formatting if I open anything in K2 such as an item. See screenshot.

imgur.com/KCHbI9s

The formatting issue can be resolved by either clearing Joomla!'s and your browser's cache assuming you are not using custom backend templates.

If the stylesheet of an older version of K2 is being cached, this can lead to a broken UI.

The user issue, unfortunately is a core issue. You can check if the users exist in the User Manager view.