I keep getting the following message in my logs, how do I fix this? javax.net.ssl.SSLHandshakeException: sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCert­PathBuilderException: unable to find valid certification path to requested target

Java cannot find your truststore file; make sure you supplied the correct VM-arguments to the web server).

My (application server) server keeps complaining about the HTTPS hostname being incorrect! How do I fix this?

Your certificate & keystore do not have the FQN (Fully Qualified name) – <HostName>.<DomainName>.
By default, the application server tries to perform a few "sanity" checks upon the SSL-connectors' URL before accepting a connection. When the FQN is part of the keystore, the application server will no longer complain.

The application server seems to work, but the client won't connect! It complains about the hostname of the server not being found!

Probably your servers' certificate has a common name (CN) that does not correspond to a hostname that can be resolved through DNS. Add the hostname of the application server to DNS.

How do I detect whether my application server uses a private hostname?

Try the command nslookup <hostname> in a command prompt. If the result of this command is the IP-address of your application server server, it probably has a public hostname. If it gives an error, like non-existent domain or such, your application server has a private hostname.