I wouldn't worry about the quill stem at all. As long as it holds the handlebar in place, it's a non-issue.
Ditto the rims. With black tires, they'll look good. And if that bike still has the original white tires, they are likely in need of replacement.
As a city bike, for running around, you can live without water bottle mounts. And that is exactly what this bike is designed for. If you want a fixie to ride over longer distances, you probably want a different bike.
It's really a pity that the Globe line didn't last. I still commute on my Globe Daily 1, and it's a terrific, inexpensive bike.