This is a very nice palette. How did you decide on the colours? I've tried creating 16 colour palettes before, and always find it hard to settle on anything that will work for an entire game.
One tip I have is one that I learnt from making music - it's really good to check colours on as many systems as possible. Phones, TV's, as many monitors as you can, Mac & PC gamma etc. Then you can tell what the range is like in terms of contrast and saturation. I spend a lot of time tweaking once I have a screenshot like this, just replacing the colours one by one, trying out different ramps (series of colours) seeing which ramps can work together (a yellow can double as a bright green or orange, for example.)
Last part is colour theory, which I probably learnt a bit about from here - the usual moving towards bluer hues on the dark ends, and yellower ones on the light ends.
Another tip is to browse palettes you like in places like colorlovers.com
Take all this with a massive grain of salt, I don't consider myself any kind of pixel artist... I just try to find colours which are a little weird in some way! For this game I wanted alien colours, so I made the hue-shifts in the ramps quite pronounced, didn't include pure black or white, and spent my most colours on hues like the greens, oranges and blues, rather than try to have a palette that covers everything.