I also have had a problem trying to update to latest version of Flash Player; after clicking the install button I get a page with this message:
Secure Connection Failed
An error occurred during a connection to admdownload.adobe.com. SSL received a record that exceeded the maximum permissible length. (Error code: ssl_error_rx_record_too_long)
The page you are trying to view cannot be shown because the authenticity of the received data could not be verified.
Also, the link you gave to Installation problems page, does not have a Download link for 64-bit versions.
I am on Windows 7, Service pack 1, 64-bit and my browser is Firefox Seamonkey version 2.33.1
Well, good news, when I tried again tonight, it actually worked! No error page, after a week or more of trying to install it and getting that same error.
Thank you for your time, anyhow.