Trivia: Bags go through scanners entering the Square. Heck, bags go through plenty of scanners throughout the city especially when travelling its subway system (only RMB2 to anywhere) and visiting the National Monuments. Any weaker bag could ooze green glob or start growing spidey bristles.
NO toilet facilities within the Square.
Trivia: The young guards stationed rigidly around the Square regards 'where's the toilet' question to be below them.
One has to exit the Square vide the underground tunnel and cross the road to get to the nearest public toilet.
Trivia: Since you're already opposite the Square, locate the post office. Buy a postcard some stamps and mail it from there. The Tiananmen Square postmark is a great souvenir.