The flag is worn backwards on the right shoulder because that's what it would look like if you were to the right of someone carrying the flag forward. The snopes.com reference in
sparky's post explains it fully.
Why do Canadian soldiers wear mustaches and some are named Patricias ??
They don't all have mustaches, that's a matter of personal preference.
The Patricias are, properly, the PPCLI, Princess Patricia's Canadian Light Infantry, named for the Duke of Connaught's daughter Patricia, with her permission, in 1914. Check out www.ppcli.com if you're interested. It is a famous and distinguished regiment, on the scale of the U.S. 82nd and 101st Airborne regiments, winning significant honours in two world wars and Korea, and every major peacekeeping operation since the 1950s, so show some respect.