Spoiler
by having one blue eye & one brown eye, just like the father.
Problem is, as far as I know, this isn't an inheritable trait. You'd think the network could have loaned some story-vetting staff from a medical show (except ABC's medical shows are Grey's & Practice; that explains it!).
Now, we know brown eye-pigment genes are dominant; one brown-eyed parent will dictate you have brown eyes.
I always assumed that people with one brown eye & one lighter-colored eye (green or blue or gray) had some problem with pigment production in one eye. A pigment production problem could be genetic, but if so would be much more likely to affect both eyes, so my guess is that the odds of a kid, even if they have inherited the same genetic pigment-production problem, having it display itself in one & not both (or neither) eye is very unlikely.
An early-development mutation in the development of pigment-production genes in one eye could also cause the color difference, but, again, the likelihood of a child developing, rather than inheriting, the same not-born-with-it mutation their father had is almost zero.
But recently I saw yet another show ("ReGenesis", one that usually has its science well vetted) where someone was identified as a chimera because they had one blue & one brown eye. A chimera in human genetic terms is someone who has a different DNA signature in different part of their body; its explained by the live person being produced by a set of fraternal twins where one got absorbed into the other at an early stage. Still doesn't explain why, since both twins have the same 2 parents, they both don't have the same eye-color, because "brown is dominant".
Oh well.
I guess you could have a case, very rare or impossible in people though documented in animals, of each twin being the child of a different father. Blue-eyed woman with one blue-eyed boyfriend, followed very closely by brown-eyed boyfriend; theoretically possible, but I don't know if this has ever been documented in humans. Fertilized human eggs produce hormones to prevent subsequent eggs from getting fertilized.
But even if you explain the eye-color thing in a chimera; that chimera's child is not going to be another chimera. Being a chimera is not an inheritable trait. I don't think.
Gotta go home now & watch more TV!

