Vatican requires you are appropriately dressed:
when you visit St Peters Basilica and the Sistine Chapel :
for both ladies and gents you may not wear shorts showing your knees and you may not wear T-shirts showing your shoulders. There are no other restrictions including shoe wear.
when you meet the Pope during General Audience at St Peters Square or Vatican Auditorium:
“golf course casual” is a perfect choice
when you meet the Pope with your church group formal dress is expected.
when you have a private audience with the Pope check with Rome’s Bishop office for US Visitors to the Vatican at http://www.pnac.org