This is an oddly specific problem I have but I'm sure its effects can be observed by anyone.

I am working on a palette for my game and the relation between individual colors is important as the color count is limited.

Colors vary in appearance depending on where they are on the screen/what angle I look at the screen from... Is there a common practice to ensure accuracy when working with colors?

I'm not totally nitpicking, I don't expect 100% precision, it's just important that some colors look lighter or darker than another color, but depending on the relative placement of them on the screen one color could look lighter, then look darker, just because I panned the image :/

About all I can do is actually check the RGB/HSV values to find out if a color is supposed to be relatively light or dark.

It's an HD TV :/

Along with any hardware complications there is always a matter of perception. Sometimes I get effects like in popular optical illusions. I was wondering if maybe I'd get more accurate results by placing the colors on a light/dark background, zooming in/zooming out or any other tricks like that.

Consider the following image:

{"name":"test.png","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/5\/b\/5b7230e0d652ce40b22dd6bb9463f7bc.png","w":400,"h":400,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/5\/b\/5b7230e0d652ce40b22dd6bb9463f7bc"}

Do the colors not look significantly different when you view your monitor at an angle? Perhaps having the colors in a checkerboard pattern exaggerates the effect?

It gets a little darker when viewed from the left or right, but the colors all still look the same.

If you're going to be distributing this to other people, all you can do is what Eric Johnson said and try to use colours with as much contrast as possible. There is so much variation in different monitors that you'll never find one set of colours that works perfectly on all of them. Best to just find one that works well enough on all.

Definitely. I think that there are probably still far too many of us using older monitors to take that for granted though. Maybe in another 5 or so years...

Many LCD monitors, even ones that supposedly have great color reproduction don't come pre-calibrated so the colors will be off. So you'd have to get a calibrator or get it calibrated...