I just returned from 17 days in Europe, Spain, France, Italy, and Montenegro and might have been a little preoccupied with pickpockets and other scams to fully enjoy my vacation.
Prior to leaving I warned the kids (10,12,&16) about pickpockets and other scams and I wasted a lot of time watching and worrying for a problem that was solved by utilizing a money belt and leaving other valuables in our room.
I'm in law enforcement so I have a tendency to be preoccupied maintaining situational awareness, sometimes to my own detriment in enjoying my vacation.
We walked around Barcelona, Florence, Cannes, Rome and we never encountered any problems. So I guess my advise is be prepared and cautious but don't obsess.
On a side note I brought some patches off my old uniforms and introduced myself to local police I met on the streets and gave them some patches just in case I need a little help from the locals. I even had a police officer in Venice take his badge off his shirt and give it to me. I also had a couple of locals in front of Casa Mila let my kids take pictures on their motorcycles with lights and sirens blasting. The kids loved it.
Be prepared and cautious but enjoy your vacation.