1

shanghai is such a safe city that is secure for even a young girl walk alone in a back alley at midnight, and people are polite and nice,
the only thing you may bear in mind is that you may encounter some young women to invite you into a bar for a drink,and you have to face a incredible bill in the end, but this is rather rare now

2

and in Beijing ,for example at the commercial centre Wangfujing, if you are invited by someone to step in an art gallery, be cautious with some 'famous and expensive' Chinese paintings he/she shows you, they are largely fake ones and will cost you a great deal to buy them,
that's it ,little tricks just for money, I don't think there will be 'real illegal' activities against foreigners,....even the Japanese(you may know why)

3

Sorry, I think Shanghai you should keep an eye on your pocket book. Lots of pick pockets there (Been there done that) Plain clothes police walk amongst the crowds watching and protecting people especially on Nanjing Road Mall and down by the Bund. Just take normal caution. As Michael Foo above says, don't buy into the so called, Art Students, who approach you on the street to take you to art gallaries for High Priced Student Art. It is a rip off. Also betware of young ladies who say they are students and want to practice their English. They take you to a tea shop and when the bill comes it can be $100 U.S.....another rip off. Those are the two main ones they try on foreigners especially single ones of just about any age.

4

Safe as in you are not going to be physically mugged, but unsafe for the reasons already pointed out - the tea scam, the art scam, the 'English teachers' from out of town scam, or any combination of them and new ones.