@Rooney
Yes, most babies are born with pale eyes and don't develop their full adult colour until the age of 3-5 months. If you can bear to wade through all the jargon, it's in the 5th para of the scientific article about eye colour here: www.ncbi.nlm.nih.gov/pmc/articles/PMC3259577/
My explanation of something "not working properly" is a bit of a simplification, especially as scientists don't have the full story about eye colour genetics yet. By "not working properly" I don't necessarily mean "total malfunction"; it's more a question of degree.
A total malfunction in one of the steps needed to make eye colour pigment, for example, could make you an albino (en.wikipedia.org/wiki/Albinism). But imagine a scenario where one of more of the steps isn't completely broken, but yet isn't working quite as fast or as efficiently as it could. So you end up making less pigment.
Alternatively, the process that gets the pigment into the pigment-carrying cells in the eye could be a tad under par. Or you could have fewer of these pigment cells in your eye anyway. Result: paler eyes.
So the bottom line is, yes, you could have a mild genetic malfunction. Or simply a more/less efficient process producing your pigmentation.
Either way, it works massively in your favour. Because it will also give you the pale skin you need to survive in the sunless wastes of the northern hemisphere. Too much pigment would hamper your skin's ability to make vitamin D from what little sunlight we get, resulting in rickets and immune deficiency.
I'm not an expert in human genetics, but I'm not aware of any secondary effects of pigmentation genes on health. There is a famous example in mice though, called the agouti yellow gene.
The agouti gene affects how the pigment gets into the hair follicles of the mouse. The agouti gene makes a substance that stops pigment from getting in to the base of the hair, resulting in a banded hair with a yellow base and dark tip.
Mice with one copy of the "yellow" version of the gene make too much of this substance. This means that no brown pigment gets into the hair and the mice are all yellow. They are also all obese, because the extra agouti gene substance also happens to block a process in the brain that controls eating. The mice don't know when to stop eating, and so balloon to an enormous size.