Due to a recent update of Chrome browser (same error occurs also in Firefox), when you open the vSphere Web Client 6.5 (Flash-based) the loved Adobe Flash plugin crashes.
This is a big problem since you are no longer able to open the vSphere Web Client 6.5. The HTML5 vSphere Client is not affected but some features are still unavailable compared to Flash version.
A Reddit user /u/theVelement found a nice workaround to fix this issue. From Windows, navigate to %USERPROFILE%\AppData\Local\Google\Chrome\User Data\PepperFlash and locate the folder called 22.214.171.124 that is the new Flash version.
If you also have a folder with a different number such as 126.96.36.199, copy the content from this folder to the 188.8.131.52 overwriting the content or just delete the 184.108.40.206 folder. This should fix the issue.
If you don't have a previous version of Flash, copy it from another computer.
You should disable Chrome auto update to prevent the automatic re-installation of the buggy Flash version by editing the Windows Registry.
Flash-based client has been already deprecated by VMware and we are waiting for the fully working HTML5 client that should be released soon.