I’ve noticed recently that a lot of pictures I have taken at night have come out with some lights having somewhat faint reflections in the pictures. An example: here is one in which several cars’ brake lights seem to be reflected nearer the top. Here’s the same with some lines drawn in matching each reflection to its source. Everything seems to be reflected around a point in the center. What’s going on? (This is a 35mm SLR camera, by the way.)
Looks like internal lens flare.
Is it a zoom? They’re more succeptable to this. Each air to glass surface increases the probability of lens flare. Still happens with other lenses, too.
Could it be the light reflecting and refracting within the several lens elements within the lens itself?
What I am referring to is best described when pointing a camera toward a very bright light source such as the sun.
Like I said. 
A good definition of flare.
I was thinking… I always have one of those UV filters on the lens. Being an additional glass surface, is that likely to be contributing to the problem?
Yes. Especially if it is uncoated or only single coated. Whenever I do real low light stuff with my f/1.2, I take the filter off. I figure it couldn’t hurt. Because there is very little you can do about those point sources flaring. If you are on a tripod, you can stop down some, but then you introduce diffraction problems and the flare will still be there, tho maybe diminished a slight bit.
A little adjustment in position often heps. Sometimes you can judge the effect (somewhat, with experience) in your SLR viewfinder.
Experiment and enjoy.