What common scams should I be aware of in Beijing?

Counterfitting is a big problem in China in general and runs a lot deeper than you may first realize. It is possible to take fake money out of a banks ATM so make sure to check your money every time no matter who you are receiving it from.

Use your judgment when people offer you their services. Many scams take place where someone is posing as an official in some way e.g. a licensed tour guide or a monk collecting for charity. Ask questions and be cautious.