We spent a month at David's place. The apartment is located in the heart of Leith, which was great for outings to Innis & Gunn, Moonwake, Fisher's, etc. Like others mentioned, it's a bit further from downtown, so be prepared to walk or grab a bus, but if you're staying in Edinburgh for more than a long weekend, it works great.
The apartment had really good Wifi (we had zero problems with it during our stay -- a record in our 5 months of living in and out of Airbnbs). The kitchen was actually a full kitchen, with plenty of knifes, cutting boards, mugs, and cups. We also appreciated the nespresso milk frother for our morning coffee! The two comfy couches were a bonus as well. The building was quiet, but the windows were on the thinner side and outside noise carried in quite a bit. The bed was small, but overall comfortable. Also, it had plenty of hangers, much appreciated.
We thought the apartment was lacking a deep clean. Though we know others have used it before us, there were quite a few stains and dusty corners and vents. The big, bright windows were great for cloudy days, but not so great in the morning, would recommend bringing a sleeping mask. Our biggest issue with the apartment was probably the bathroom, as it was lacking a shower door (had a temporary shower lining), workable outlet, trash bin (in the host's defense, seems to be a common theme in Airbnbs, but would be nice for disposal of floss, qtips, etc.), and an efficient heat source. Sounds like the host is aware of some of these issues, so hopefully they'll be fixed for future guests.