Windows server 2003+vista pc+problems with GPO

After joining vista business laptop to domain (win server 2003)and after this pc user moving to local administrators group, we noticed these problems:
1) Don`t work login script
2) Sometimes we are losing connection to internet (Intranet works fine always!).

There are problems only after domain user migration to local administrators group. When he is a standart user in this laptop – all works fine.

Can anyone help in this situation?