"When I use the iPhone VPN to connect to my company network, both iShare and Safari say "Can't find host" when I try to connect to my SharePoint server."
Depending on your VPN configuration, some orgnanisations have problems with DNS Resolution from the iPhone. In non-geek terms, that means the iPhone can't find the server you are asking for.
You can try using the Fully Qulified Domain Name (FQDN) or IP Address instead.
A Fully Qualified Domain name is the common name of the server, with the your company's Active Directory domain appended.
For example, if your SharePoint server is usually located at http://sharepoint/ , and your Active Directory Domain is MyCompany.internal, try connecting to http://sharepoint.mycompany.internal
If that worked for you, then you should ask your SharePoint Administrator to add an Alternative Access Mapping in SharePoint for the Fully Qualified Domain Name. This will ensure that SharePoint talks nicely with iShare.
"When I connect to my site, the SharePoint lists appear, but the sites do not. I also see an error - 'NSUrlDomainError -1012'"
This can be caused by using an incorrect username/password, or when your SharePoint user account does not have sufficient priviledges. Try giving the account 'Contributer' priviledges in SharePoint.
"I can open a SharePoint site using iShare, however when I click on any of the subsites, lists or libararies, I get the error: 'Can't find host' "
This is most likely caused by a DNS alias for your SharePoint site and/or a Firewall between you and the server.
Commonly this is a result of your site having a public/extranet URL address that is translated to an internal address
For example:
http://extranet.mycompany.com -> Translation by Firewall-> http://SharePointHostname/
http://intranet/ -> DNS alias-> http://SharePointHostname/
Essentially your sharepoint site address is being automatically renamed on each request as it is passed to the SharePoint server. Usually in a web browser everything can work fine because most links are returned as relative path addresses (e.g. /Client Projects/Client name/Documents/ )
However when iShare talks to your SharePoint server via Web Services, it often gets told the full absolute URL:
e.g. http://intranet/Client Projects/Client name/Documents/
When iShare tries to connect to this inaccessible internal URL the problem is revealed.
For the internal DNS alias scenario, often your adminstrator just needs to add the alias as a default Alternative Access Mapping in "Central Administration > Operations > Alternative Access Mappings".
After this is added, search may need to be re-indexed before search results will appear correctly.
Where a firewall and link translation is involved, you may need to make changes to both your SharePoint Alternative Access Mappings and your firewall settings. Here's a good article to get you started:
http://blogs.msdn.com/sharepoint/archive/2007/03/06/what-every-sharepoint-administrator-needs-to-know-about-alternate-access-mappings-part-1.aspx