For the sake of argument let's say the period is sometime right before the Peloponnesian war. So not only are there cities in Greece and turkey ( please excuse the use of modern borders), but also far away colonies and their cities. Could a man educated in culture and dialect of each locality simply fake citizenship in any city. Or was there an identification system for natives?
I can only speak to Athens to this, but it seems entirely plausible to me that other cities would have something similar. First, we have to acknowledge that even large poleis would have a relatively small number of citizens. Athens, a comparatively large one, had something in the order of 50,000 citizens (men) at the start of the Peloponnesian war. So we are never talking about a huge city. That said, there were still mechanisms in place. In Athens, the area of the polis (including outside the actual long walls) was organized into 'demes', each headed by a 'demarch' who served the combined function as a sort of mayor and chief returning officer. Essentially, their job was to maintain the citizenship rolls for their deme.
What this means in a practical sense is that pretending to be a citizen of a polis in that polis seems impractical, as you would have to have someone vouch for you in public, while maintaining the secrecy of any bribes or such you paid. How long could such a charade last?