That’s a New-Law tenement at the corner of 33rd Street and Third Avenue. The 1901 New York State Tenement House Act was such a vast improvement over the 1879 Old Law that it created a new and desperately needed class of building in New York: the livable apartment for people without a lot of money. Unlike the narrow airshafts of the Old Law dumbbell tenements, the New Law buildings had real light courts, a lower percentage of lot coverage, proper plumbing requirements, and so on. This building was constructed about 1920, a few years before the 1929 Multiple Dwelling Law banished the word “tenement” from new construction.
I’m not going to make any jokes about the corner chicken-finger shop being called “Sticky’s Finger Joint” as I’m pretty sure that joke is intentional on the part of the restaurant owner. On the other hand, the jokes about a shop selling marijuana paraphernalia and beer immediately next to Sticky’s and a cookie shop and two doors down from a McDonald’s seem too easy. It looks like a busy half-block.
There are certainly more than two apartments per floor, so I have to assume that there are additional fire-escapes on the far (west) facade or on the south facade, which has a light court. The structure of the building is wood joists supported by masonry bearing walls and the odd steel beam where gaps in the walls are needed for the layout, so fire egress was a critical issue in design.
The facade is quite plain but has some pretensions to style. The most obvious is that it’s gray or light tan brick under the grime, rather than the dark red of common brick. There’s some ornament at the second and sixth floors, as well as quoins up the corners. The terra cotta water-table below the sixth floor windows is nice and probably gives some hint as to what the missing cornice looked like. Most likely, the parapet was lower when there was a cornice there and it was raised to handrail height when it was rebuilt. The repairs on the lower portions of the facade (mostly lintel replacements, it looks like) seem to match the brick well, or maybe reused the original brick.
Excluding my comments about the retail, I’ve written some 300 words so far on this building and they boil down to: this is as average a New York apartment house as you’ll see. It’s plain and has old-fashioned structure but it functions just fine.