Hi Mike,
Yes, I have tested using the farm account as well as my own. Both have full access to the entire web application and are local admins on the server. I am also site collection administrator on the site. The library inherits permissions from the site
collection. So I don't think it's a permissions issue with my account or the farm account.
I can see all of the content, as shown in my screenshot above. However, the SharePoint object model (via PowerShell) cannot find the other versions (for example versions 1 through 8), it only sees the current one (version 9).
I replaced the actual usernames with my own for the above example. Here's another one:

In this case, version 2.0 is accessible via PowerShell, but version 1.0 is not.
A coworker of mine suggested that this might be due to the site being migrated from WSS 2.0 into this WSS 3.0 site.