What permissions should the account for MS SQL Server Agent have?
You also need to verify that the AD account will have access to the parts of the file system that it might need.  We ran into this awhile ago, and I don't remember which jib had an issue.  Could have been backup, or something else. 

If you're using SQL to connect to remote SQL Servers, then it depends on if you are using linked servers.  Linked servers use the SQL to connect to the remote server.  If you open a connection directly on the remote server, you'll need a Windows (probably) or SQL authentication login on that server