An egg's color is added last in the egg laying process. You can think of it kind of like a car being spray painted. An older or younger hen may have this process interrupted somehow, resulting in speckles, smears, odd colors, or even completely colorless eggs. They're just like wind eggs- they happen sometimes. There's probably nothing wrong with your bird, so don't worry.
I have one hen that lays eggs just like that, and another one that puts the brown speckles on a green egg. It's just a glitch as described above. And yes, my speckles wash right off, another reason not to wash eggs. Speckled eggs are quite cool!
We have one bird that lays eggs like that - maybe not quite as many speckles - from the first day she started laying. I think they're the prettiest ones we have.