Use the systemd journal to provide an improved GNOME System Log. This will be especially useful in the case of systemd for the user session, as log messages (from stderr or stdout) from individual applications will be logged in the journal directly rather than going via gnome-session. Using the journal API, it is possible to provide much more information about log events than a traditional unstructured logging scheme, and GNOME Logs can take advantage of that structure when presenting log messages to the user, from the simple case of providing selectable categories, to constructing complicated search queries.
I'm proposing this on behalf of David King, who is working on this and just did a first tarball release.