when mixing/mastering then the advice often given is to try it on lots of different systems and if it sounds good on all then it should be fine. if it doesn't then you are probably doing something slightly wrong, but not necessarily:
different monitoring setups will have different frequency peaks and troughs (and the room you are in will have some effect too as some frequencies will bounce back and multiply, some will cancel) this tends to lead you to inappropriately boost some parts or attenuate others. to get the best possible sound you want your setup with as little reverb from the room as possible (so a largish room with some sound dampening of some sort), good speaker positioning to avoid phase cancellation and a very flat frequency response from both your amp and speakers.
this is hard to achieve but its still possible to do a very acceptable job with non-optimal gear by simply listening to a huge amount of the very best produced music you have on your normal setup and making it sound close to that in terms of balancing. there will still probably be issues when then trying it on headphones so re-tweak slightly to fit them and try again on the main setup. its hard to describe this stuff, but you should sort of 'know' when you've got it good on both and you can assume that it should then sound good on most other systems too, the more you use the better you can get it but you need to know all of the systems well through listening to lots of your favourite well produced albums as a reference.
problems with the mixing almost always come to the fore when listening on different gear and as long as you know its not the setup thats at fault (because your favourite records sound bad in the same ways) then you can fix it and improve the mixing of your track.
hope that is clear-ish and helps!
