These appear highly inaccurate or something weird is going on. Search for Istanbul and see all the postal codes in Istanbul province (Istanbul = Adm1). I haven't found a single one yet that's actually in the Istanbul province. This leads me to believe there's some serious data problem here, either with the adm columns or the lat/lons.
I will add a warning to the readme that the lat/lng are far from perfect. At the moment I don't see how they could be improved with the data available.
I don't think there's an accuracy problem in this data set, as all 51,193 points are in Turkey. Of 28 locations in Istanbul, 2 (Anadolufeneri Köyü and İmrendere Köyü) are actually have correct coordinates.
I believe something got mixed and now we see some random, but still in Turkey, coordinates. Is there a way to go down to the source and fix this?