You don't mention what version of SharePoint you are using. There are limitations on the version of SharePoint you can interact with using the new BizTalk 2013 adapter with Client Side Object Model (CSOM). The CSOM only allows you to interact with SharePoint services on SP2010, SP2013 and SharePoint Online. It's even more limited with CSOM disabled - this means you would be using Service Side Object Model (SSOM) and you are limited to only SharePoint 2010.
The BizTalk 2013 SharePoint Services Adapter using CSOM requires you install Windows Identity Foundation, or turn it on as a feature, depending on which version of the OS you are running the BizTalk Server.
Ensure you've correctly setup a proper receive location as well as the send port (be it static or dynamic): http://msdn.microsoft.com/en-us/library/jj735586(v=bts.80).aspx
If you've chosen to disable CSOM on the SharePoint Adapter, you would have had to install a service on the server hosting SharePoint (assuming it's different to the BizTalk Server). In this case you need to ensure the IIS apppool hosting that server uses a domain account. In this scenario (with CSOM disabled) you can also get access denied issues if you have a double hop. If there are three computers involved (BizTalk Server, SharePoint Services and SQL Server) and you haven't enabled kerberos/setspn (on the domain accounts for SQL and the AppPool account hosting the sharepoint service) then you will have authentication issues. You can determine this by checking the IIS logs. You would see in your IIS logs a failed status code, eg. 401.2, followed by a 401.1, following by another 4xx error.