This is a problem that is common any time there are two repositories. They are just going to get out of sync at some point in time. On to your questions:
Are there more such cases? My guess is probably, but I have never come across any.
Is there something we should do about this? In my opinion, if anything should be done, the deprecated module should be taken out of the ActiveState distribution, but seeing as we don't have control of that distribution there isn't much we can do.
Can we take this (and probably similar) modules from the ActivePerl distro and upload to CPAN? Sure, but I don't see why we should. This would just further perpetuate the deprecated module. In your case I would try getting an ActiveState build and run your clients script through that.
Comment on Re: Env::Array in ActivePerl but not on CPAN
It would be good to discourage people from using this module, but as whether you should discourage your client from using it depends on your relationship with the client.