Michael,
Thank you for your reply. Your workflow wont work for me, but I think that I may be able to adjust it so that it will work.
The original images on my map have been scanned so that the edges are not pure "black", a single color, and in some cases the edge color may be the same color portions of the image such as water. Therefore I cannot just assume a single color is "no data" nor can I use a threshold to set "no data."
But maybe this is what I can do:
1. Build footprints around each image.
2. Create a negative buffer of about 35 pixels so that it is large enough to remove any border.
3. Import the "shrinked" images
4. Add all the original images under the shrinked images.*
5. Create a image from that.
Now I just need to figure out the best way of doing this in ArcGIS
*The cropped images will be on top and the originals would be on bottom incase I remove too much overlap in step 2.