Random 404 Error on Website

So I backed up my website, moved to a new hosting & domain and imported it.
I had the website up and running then came the 404 Error Website not found. It went away an hour later and the website showed up again, it has been doing this for a few days now.
I got people to try the domain & around 1/3 got the 404 error (some could access it a while after it failed). It seems to randomly fail on people & I can’t figure out why. Here are some recent very common error logs,

[Thu Aug 15 11:17:22 2013] [error] [client 66.249.74.44] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/blog
[Thu Aug 15 11:17:22 2013] [error] [client 66.249.74.44] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:17:39 2013] [error] [client 95.83.253.231] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/favicon.ico
[Thu Aug 15 11:17:39 2013] [error] [client 95.83.253.231] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:19:01 2013] [error] [client 66.249.74.78] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/sligo
[Thu Aug 15 11:19:01 2013] [error] [client 66.249.74.78] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:20:31 2013] [error] [client 66.249.74.68] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/oxfield
[Thu Aug 15 11:20:31 2013] [error] [client 66.249.74.68] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:20:43 2013] [error] [client 66.249.74.72] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/sligo
[Thu Aug 15 11:20:44 2013] [error] [client 66.249.74.72] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:21:36 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:21:36 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:21:38 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:21:38 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:21:38 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:21:38 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:21:38 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:21:38 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:21:47 2013] [error] [client 66.249.74.54] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/sligo
[Thu Aug 15 11:21:47 2013] [error] [client 66.249.74.54] File does not exist: /usr/local/pem/vhosts/153232/webspace/siteapps/WordPress-56630/htdocs/error_docs
[Thu Aug 15 11:32:42 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:32:42 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:32:42 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:32:42 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:32:42 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:32:42 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:32:42 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:32:42 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:33:43 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:33:43 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:33:43 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:33:43 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:33:43 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:33:43 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:33:43 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:33:43 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:54:17 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:54:17 2013] [info] Loading certificate & private key of SSL-aware server
[Thu Aug 15 11:54:17 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:54:17 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:54:17 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?
[Thu Aug 15 11:54:17 2013] [info] Configuring server for SSL protocol
[Thu Aug 15 11:54:17 2013] [warn] RSA server certificate is a CA certificate (BasicConstraints: CA == TRUE !?)
[Thu Aug 15 11:54:17 2013] [warn] RSA server certificate CommonName (CN) `plesk.com’ does NOT match server name!?

It seems to be searching for files that aren’t there but not always as most of the time the site works for people.
I thought the problem might lie in the theme I’m using which hasn’t been update in 3 months but WordPress has recently. My hosting company don’t seem to think this cound be the issue.
Any help or advise is welcome, my website is https://www.condohphoto.com

Thanks, Conor