Since Git notes do not work as normal branches, it can be a little cumbersome to push them back and forth to a repository when you are trying to collaborate on them. Since you cannot just fetch and merge the Git notes branches as easily as with other branches, a clear recommendation is to build some tools to add these notes so that you only have one server adding the notes.
A simple, but value adding, note could be information about Jenkins builds and testing. This can be valuable when you have to reopen a defect. You can then actually see in the repository which tests were executed on the commit hash.