Is a transit visa required if my Hanoi - Toronto flight has a domestic leg from Shanghai to Beijing?

You don't need a transit visa for the domestic leg from Shanghai to Beijing. According to the exit-entry law of P.R.China, transit visa is not required for those aliens who are in immediate transit through China on continued international flights, who hold connecting flight tickets and have seats booked and who stay for not more than 24 hours within the airport of the in-transit city (the transit cities can be two or more cities within Mainland China), but they shall apply to the border check-posts for stop-over permits.