Hey, wildbug! Interesting idea. Unfortunately, I don't think this is something that you can do. We don't currently support a way to run more than one module or move it into different locations. But, I can understand how this would probably be a good solution.
You can add a rss text box to the green shaded area in the right column. Then copy the address from the address bar that shows up when you click on the rss button (opens new tab/window) on the lower left of the activity module. Paste that into the url box when you edit the rss box. This will give you a new activity feed which will show on all pages. If you set it to show details then pix , etc. will show. Now the trick is to block its display on the main page if that is what you want-I'm working on that ...maybe someone else has worked that out-been searching but have found nothing yet. The other difference is that the "more" button at the bottom of the rss feed redirects back to main page rather than additional activity history. That should be able to be fixed, too. Like Eric, I think this an interesting idea. Hopefully those two things can be "cleaned up".
EDIT: it's just a report- no way to enter update.
Thanks for the responses. I've given up on this idea and will just put it in the right column on all pages. Too complicated to figure out...