Q:

Is it biologically possible for an adult's eye color to change?

Can it be that the adult eye can change color? Specifically my question is about a unilateral color change, such that the color of one eye remains constant, while the other changes color over time. Can this happen? Or can it be related to light-scattering, or an illusion of some sort?

A:

Short answer: The genes that encode eye color do not change, but the pigments in the eye can change due to external factors like diseases of medication.
Long answer: Yes, it is possible that the eye color of adults can change, and it can also only happen to one eye. It is then called Heterochromia. There are two possibilities for different colored eyes, either congenitial (genetic) or acquired. Since you ask only for eye color changes in adults, we can skip here the genetic reasons, as these show up in kids already. If you are interested in them, have a look into the Wikipedia article on Heterochromia.
The basis for our eye color is genetically determined, changes can later occur due to diseases (so if one experiences a change in eye color, it is always a good idea to consult a doctor) and also due to medications. 
The eye undergoing a change in pigmentation can either lighten up or darken.
Fuchs’ Heterochromic iridocyclitis: (also known as Fuchs’ Heterochromic uveitis) The change is caused by an eye infection with different microorganisms like Toxoplasma gondii, Herpes simplex virus or Rubella (an probably others) but it can also have an autoimmune pathology. See reference 1 and 2 for more details.
Horner's Syndrome: This is a syndrome which mostly occurs in kids after damages to some nerves. This can lead to insufficient signals towards the pigment production and heterochromia. Rarely this can occur also in adults, where this is called acquired Horner's syndrome, see reference 3 for details.
Pigmentary Glaucoma: In this disease (also known as Pigment dispersion syndrome) pigment cells from the back of the iris float are seperated from the original place and float through the aqueous humor of the eye where they can produce pigment which over time changes the appearance of the eye. See reference 4 for more details.
Medications: Some of the medications against glaucoma (the prostaglandins latanoprost and bimatoprost) can cause a deeper pigmentation which will not always diminish after the end of the treatment. See reference 5 for more details.
Cancers: Some cancers as melanoma can also cause heterochromia, either when they are darker pigmented that the eye or when they are not pigmented. In both cases they influence the eye color. See reference 6 for more details.
References:

Fuchs' heterochromic cyclitis: review of the literature on the
pathogenetic mechanisms.
Associations of Fuchs heterochromic iridocyclitis in a South Indian
patient population
Acquired Heterochromia with Horner's Syndrome in Two Adults
Pigment dispersion syndrome and pigmentary glaucoma – a major review
Incidence of iris colour change in latanoprost treated eyes
Diffuse iris melanoma: Report of a case with review of the
literature

