*climbs back on the genetics platform*
To give yourself a little more leeway, you could just argue that it's several genes at play. Most phenotypical things (hair color, eye color) are several genes. Thus it's possible for two families of brown eyed people to suddenly produce a blue eyed child. It's several genes at play and when they line up just right, you get someone with blue eyes when it's unexpected.
Originally Posted by Molly
If you want to play it like that, you could say that as it's several genes but primarily recessive (like blue eyes), you can get Muggle born wizards and witches, and pure-blood families generally producing wizards and witches, while half-bloods would be more of a crap shoot.
Dimples are actually one gene, I recall. Very random thought. Genetic diseases and defects occur because something went wrong in a specific part of the chromosome (something snapped off, something repeated too many times, something flipped itself, etc, etc.)