Quick post cause my googling didn't point me in the right direction but as usual Jason Nash did.
Had an issue with the vSphere 5.5 web client on the VCSA in my lab where it would launch from a Windows machine but not from an OSX machine even with the plugin installed on the Mac. Here's what I saw when it was broken.
Turns out it's am issue with the environment variables for JAVA_HOME on the VCSA. This KB article walks you through fixing it, but doesn't mention the case where it works in Windows but not in OSX so it can be a little misleading. Once you restart the web client and log back in you will be able to use the HTML5 client on OSX in all it's glory.
Hopefully this helps people find the fix they are looking for. Thanks for reading!