Multisite content visible but not editable

I've been asked to take over management for a multisite installation. The plan is to move it to a different host. Since this is my first experience with multisite, I have logged in and looked around how things are set up. I noticed something odd: The theme (AIT Directory) has implemented a custom post type called 'items'. When I go to the subsite with the items, I see all 200 of them (both in the back-end and in the front-end). But when I try to open them in the back-end, I get an error message that the page does not exist. I can't open any of them.
Do you have any idea what could be going wrong here, and how I could fix it? I should add that for standard content (posts/pages), there is only one page, but that I can edit. I realize a them update might help, but that is not possible at the moment, as the changes are enormous and the risk of crippling the site is high. I first need to secure the content.