Syslogd message - File Does not Exist

From my understanding, /usr/local/www/ is the path where the login page exists and has the banner files. This is like the apache home directory where your required files exist. So this location contains the items what you see on the GUI or the browser.

Here's what I think could have happened, that folder or the file existed on your previous version, but not in the latest code. This could have been because of the upgrade on the bigip.

And its obvious why you are seeing it on local6, because local6 file logs the details of httpd, again Apache related.

But what wsman is about, I have no clue.