I've started watching Kara Para Aşk, and I can't help thinking that in whatever dialect/accent the cop's girlfriend has, she uses what sounds like an American R ("retroflex approximant," also heard in Dutch and some varieties of Brazilian Portuguese, I think), especially in [V]r[C] situations (closed vowels where a vowel is followed by an 'r' and then by another consonant). For example, I know that "nerede" is pronounced closer to "nerde" in normal (non-careful) speech, and it sounds like she's saying "nerde" with an American 'r.'
Am I just hearing things?
Check out what I wrote above. It is a little more specific (because you are right...they aren't the exact same sound except in some places [in Istanbul and Ankara I have tended to hear it like the American one...not in the Aegean region or the Western Black Sea region at all which is pretty interesting!]). It is a phenomenon mostly reserved to younger people too, like you said.
I have looked up the IPA symbols and the term rhotacized in Wikipedia. I guess V and C stand for vowel and consonant. X might stand for any sound but I have no idea about #.
ɾ̝̊ should be the voiceless version but I couldn't figure out the difference. How could it be voiceless? Is it voiceless when it's in the end of the word? Then does # mean blankness..? :D
But also we don't necessarily roll the R when it's at the end. Sometimes we may pronounce it very softly that it's almost a vowel. That's why we pronounce it like ş. Many people here confused bir with /biş/. Maybe you mean this by voiceless.
Something very very very important to remember is that if you have a vowel before 'r', that vowel is still fully pronounced. Americans in particular struggle with this, the classic example being the pronunciation of "Bursa." If not pronounced correctly, a lot of people end up saying "börsa" or "borsa." (the latter means stock exchange, which is nothing like Bursa at all :D)