I have one project where I can't use the new issue layout to assign users. In the other projects I have (with the same users and the same permission scheme) that works fine, but in this one project the Assignee field is read-only and I can't even try to type into it.
The only way I can assign users in this project is to revert to the old issue layout and use either the Assign to me link or the ASSIGN button.
It must be something I have done, but I'll be buggered if I can see what. The project is a JIRA Business type, and contains multiple bespoke issue types, one with its own custom workflow.