I have Blue Jeans 1.6 installed and it keeps listing an older version as an upgrade.
This is probably a mistake. I recommend updating the extension in the Google Chrome Extensions Store. You can find the link posted here. After it has been upgraded, Refresh the client and watch its status. In case it says the version is wrong, don't apply the update. It should probably be fixed in the future.
Store link: https://chrome.google.com/webstore/detail/blue-jeans/iedelpfmeejalepbpmmfbfnfoeojohpp/reviews