Yes there was noise at night but thats a great thing! Trastevere is such an alive neighborhood, we loved it. The windows in the apartment look to be double glazed anyway and any noise that got through wasnt enough to bother us. The apartment is a nice size and has plenty of space for opening a couple of suitcases and living around. Awesome restaurants and bars so close. Most of Rome's tourism hotspots a half hour walk away. The host met us onsite and was very generous with his time in explaining our location in relation to city features.
There is 1 flight of stairs to consider if you're with full size suitcases like we were. But you only drag a suitcase up and down once right?