System: a fresh ubuntu dapper install. The sudoers file looks like this:

---sudoers---
Defaults        !lecture,tty_tickets,!fqdn
root    ALL=(ALL) ALL
%admin  ALL=(ALL) ALL
---sudoers---

All following commands are executed by a user who is member of group 'admin'.
The output of command
sudo bash -c env | grep HOME
is
HOME=/home/<calling_user>

Now, if i append '%admin ALL=(ALL) NOPASSWD: /bin/bash' to the sudoers file and run the above command again no password is required, but the output is empty.
Why is there this different behaviour? This has bad impact for X applications: Only if $HOME is set, the <calling_user's> .Xauthority file is found and access to the XServer is granted. Without HOME being set (just by using NOPASSWD), access is denied.