It turns out that there is another requirement for the bug to manifest: "Ending Screen" must be unchecked for the slideshow set to use for Impromptu Slideshow. Revised steps to reproduce:
1) Slideshow module
2) Click on default template
3) Uncheck "Ending Screen"
4) Save as a user template "Bug"
5) Set template "Bug" to be the one used for Impromptu Slideshow
6) Develop Module with a folder selected with 174 images
7) Click on 4th image in filmstrip
Actual Result: The slideshow starts with the 3rd image in the filmstrip.
Expected Result: The slideshow will start with the 4th (selected) image in the filmstrip.
Can anyone else confirm?
Actually, the bug only manifests when both "Intro Screen" and "Ending Screen" are unchecked. If either one is checked for the template used for Impromptu Slideshow, the bug doesn't occur. Very, very odd bug.