What is the screen capture supposed to show?
Some general advice on moving books to a newer version:
If you don't have to, don't do it. It's full of little traps, like text that will reflow behind your back when you click on a frame to edit. This is caused by differences in the text engines from version to version and only shows up on text thathas been touched, but it can result in differnt line endings and pages that flow differntly or overset text, so be VERY careful. The problems could be pages away from where you are working.
If you must update, I recommend exporting all of the legacy files to .inx or .idml (depending on the version) from the original files in the version in which they were created, then open each of these in your new version of ID and save as new .indd files with new names (which is going to screw up inter-file cross-refs). Make a new Book from the new files. As a side effect, the trip through the intermediate file will force all stories to recompose withthe new engine when you open them, so you'll get that out of the way, but you still need to look for problems.
The screen shot is to just demonstrate that the nesting is working in one place but not another. I will try going to interchange first. The problem with keeping in one version is that we have hundreds of books archived from version 1 through 6 so I can't keep all versions on my computer. Also most of us only have one version so I can't always open the books in the version they were created in to interchange.
I just wanted to make sure this was a conversion bug and not a CS6 bug on moving forward.
I'm not aware of a general problem with nested styles in CS6, and I think we'd have heard a lot of complaining if there were.
The screen shot is to just demonstrate that the nesting is working in one place but not another.
It seems to work for both numbers -- were there supposed to be more green phrases?
Perhaps all this needs is a little nudge in CS6. Try changing a very minor thing in the paragraph style -- say, "underline stroke width". That will trigger a refresh of the styles-where-in-use; perhaps your nested style will hitch along.
Something else you could try is using Find-and-Replace, "replacing" the style with itself (but be warned, this might fix the issue but also clear out any and all local formatting applied to these paragraphs, which may be a bit more than you asked for).
The problem with keeping in one version is that we have hundreds of books archived from version 1 through 6 so I can't keep all versions on my computer
Why not? I have an archive stretching back to the mid-90s. I have InDesign CS through CS6 on one computer. Admittedly, CS and CS2 are in a VM, but there's nothing whatsoever stopping you from having all of those versions of InDesign on your machine, and continuing to use the original application to revise books in the future. Heck, sometimes I have to open stuff in PageMaker to clean it up before importing to InDesign. So yeah, I have PM installed in virtual machines as well, not to mention Ye Olde Mirror-Door G4 which I still start up on occasion.
Is is the case that the nested style is applying the green tint, but not whatever bold-ish font is being applied to no. 1? Can you post a sample file for us somewhere to download and examine? I've not experienced this, and I'm a pretty heavy user of nested styles, but I usually keep files in their source format. And of all of the files I have hanging about in CS5 or CS5.5, none of them exhibit the behavior that yours does when I open 'em up with CS6.