If you can't make it to the Vatican Mass on a Sunday, Saturday or Monday are also great days to visit. You will noticed a sea of chairs in St. Peter's Square starting on Saturday night and the chairs will remain there until mid day Monday.
Go ahead and take a seat. You may not have made it to mass, but you can still experience and take in grandeur of the square. It is definitely worth sitting down and relax for a moment before you fight your fellow tourists.