If by dodgy you mean areas where people regularly steal and harass, then no, we don't.
What city do you live in, by the way? The only city I know of deservedly with this reputation is Singapore.
I'm deliberately singling this one out as a point of pride:
Where in Warsaw can't you walk down the street reading your iPhone?
I'll concede pickpocketing can be an issue on buses, and racism is very much an issue in present times. Issues with muggings, though?