I just recently managed to extend my residence permit in Kadıköy.
Due to the fact that I was facing some problems, I am writting this thread so that others can be prepared.
In order to extend/renew your residence permit every foreigner has to get a fixed date for his appointment in the internet. This is nothing new but the problem in Kadıköy is that the local police station (Kadıköy ilçe emniyet müdürlüğü) is giving you dates which are Protected content in the future. (In my case, my residence permit extended in October and they gave me the 23th of January Protected content the soonest date!)
If you are staying this Protected content in Turkey without leaving the country (or you just leave ones-depending on your nationality), you are facing no problem at all and shouldn't be bothered because your residence permit is valid until the date of your appointment (even though technically your residence permit has already extended). BUT if you have to leave the country from time to time (work or private), you are treated as a normal tourist which may give you some problems.
(If you are leaving f.e. Turkey two times in this Protected content period, the pass control people do apparently not except the letter of the police station so that they tread you as a normal tourist and maybe do not let you back into Turkey the second time you want to enter the country). This is just what the police men in Kadıköy told me as I informed him that I have to leave Turkey at least two times in this 3 months due to business trips.
This topic is quite complicated and it took me quite some time to understand everything myself (especially in Turkish!) so I don't want to get too far into details but the fact which I wanted to point out is that you should get a date for the extension of your residence permit in Kadıköy some months before your residence permit is expending to avoid those problems.
I had to come several times back to the police station and speak with the manager (müdür) to get a sooner date and afterwards everything went well. If you spend 5 minutes in the internet 2 months before your residence permit is expending to get an appointment you are saving a lot of nerves and time though.
P.S.: By the way, this is only for Kadıköy and depends on the local police station. In Kartal they give you a date two days later...
I hope this is helping somebody as it would have been great if I would have known this before.