John,
I came in here looking for help on the greyed-out paste-link button but stumbled onto this question and am glad to be able to help. The solution to your question is not only simple, but one of my most used tools in Visio (though I cannot guarantee my solution works in anything older than 2003 or other than Professional).
Solution 1: In 2003 and 2007 Pro, add the "format shape" toolbar.
My preferred solution however: R-click in the top toolbars - select customize from the bottom. Choose the "commands" tab up top, choose the "format shape" category and select the last command called "layer".
This will not only allow you to instantly see which layer the highlighted selection is on, it will allow you to easily change layers. I also add the second from last command called "layer..." which allows you to add new layers thus bypassing the annoying R-click - format - layer while opening up the same window.
The first layer button will allow you to select or change the layers without opening another window as it makes selections via a pull-down which drastically speeds up my drawings!
Enjoy!
Shayne
shayneneal at gmail.com