Unwanted spots and reflections with canon EF 50mm f1.8 II night shoot

Did you try taking the filter off? Could be that the filter is causing reflections on the glass - the lighspots certainly appear to be reflections of bright light spots in the shot so try shooting without the filter.
Modern DSLRs already have UV filters built in so the filter is mostly just a screen protector and not much else - further if it is a cheap filter and not multicoated then there is a very strong chance that it is the cause

 

Those are most likely lens flare or reflections from within the lens. This can happen when you have brights lights in an otherwise dark scene. The light is reflecting off of the sensor, or part of the lens, then bouncing around in the lens. It's not dust on the lens or on the sensor etc.

Part of the problem is probably due to your cheap lens. I don't think they put a lot of anti-reflection coatings in the 50mm F1.8 lens. That's why it's $80. Also, the UV filter could be another cause of these reflections.

Another factor might be the aperture you are shooting at. Most lenses are weakest at the extremes...their max aperutre for example. This lens, for example, will usually give much better quality at F2.8 than it will at F1.8. I'm not sure if that would help reduce the flare though.