On the plus side, the apartment is lovely, with a view onto the Place Monge. It's convenient to the Metro: about 20 feet from a station. The kitchen is nice, if you plan to eat in. (If you do, you can shop at the outdoor market that is in the Place Monge 3 days a week.)
There were some issues with the water heater, but I was able to work with it.
The main problem is that the apartment is on the very top, sixth floor of the building (seventh floor for an American)... and the elevator is broken. That's a lot of stairs. This is particularly a hassle when you first arrive and have heavy luggage, but it's never especially fun.
I chatted with other residents of the building that I encountered on the stairs, who told me the elevator has been non-functional for "about two months." Yet no mention was made of this in the ad when I booked the apartment: a sixth-floor walkup typically rents for much less than an apartment served by a lift.
I asked the management company (that handles this unit for the owner) about the elevator -- twice -- but never got a reply to that specific issue. I assume that at some point the elevator will be fixed, so this won't be a long-term issue.