Report from Oct 23 : I received my approved chinese touristic visa from Tbilisi.
I am a french traveler, and I got a double entry visa, for stays of 10 days each - short, I know. I was very sceptical my application would be approved at all for two reasons.
The first reason is that I stayed for more than 2 weeks - namely 5, in Turkey. I had read that they don't seem to appreciate this, and two visa agencies from Hong Kong told me that would not be approved. My turkish exit stamp was somewhat hard to read and in a weird place, maybe that helped.
The second reason is that I had to "lie" and say I had never visited China before even though I did 15 years ago. If you say you have been there you have to provide details about this stay, most importantly the visa number. I have had two passports since, and did not photocopy this visa, so I could not provide these details.
I applied on a Friday and got the visa on the monday afternoon with the express treatment, for around 151 GEL or about 50 EUR right now.
There is no appointment system in Tbilisi so you have to show up early and queue. It is an annoying process, as people don't stand in a clear line, and people will pass in front of you to join other people already waiting, or start waiting on the other side of the door. For visa applications, it opens at 9am on Mondays, Tuesdays Wednesdays and Fridays. I got there around 7.30 AM and there were already about 20 people waiting. A guy - not an official employee, was keeping a list in a notepad, everyone said I should get my name written in it so I did - I was number 44 in that list. As the hour closed by many people had joined, most of them in front of me or on the sides. The guy started gathering passports of everyone, me and two georgians refused. The official guard finally showed up about 10 minutes before opening, hardly managed to get everyone to finally line up properly. To my surprise a woman (again not an official employee) had the notepad list and checked that everyone was in the right order, and people obeyed. So I got around number 44 in the queue. Before letting people in the staff came out, counted the people there. Those after number 40 or so were told to come back to apply at 2pm, and we had our passports taken by an official staff - I asked to see a badge and the employee was very nice about it. So I came back at two, and waited on the side of the door, not in the somewhat formal line because that one is for passport retrieval. It's a weird process but they were letting people in in parallel for visa applications and retrievals. I was stressed but they did let me in, and I think that the order was respected.
For the retrieval I showed up at around 1.30pm, and counted 14 people in front of me. A few had passed in front of me by 2pm, and there was this second group waiting around the door for late visa applications - or skipping the line, can't be sure. It was not too bad and I was out of there by 2.45 I think. The line was quite long by 2pm, so do get there early.
Note that you will need to have the exact change in GEL. I did not, so I had to ask people for change. In the end, the guy behind me, whom I was sure was trying to pass in front because he was standing 1cm shoulder to shoulder with me the whole time, helped me with an extra GEL I was missing and would not accept me to repay him after - so he was nice in the end. I guess I have not been here long enough to understand the Georgian attitude

I have been very surprised at how little people smile, but it does not seem to indicate rudeness or being annoyed, be warned !
The employees are efficient and speak English - except the guard, and one even speaks fluent French.
Good luck everyone !