The green shine is caused by tapetum lucidum. My Dachshund has it as well, although in both eyes, and the shine is actually very dim. As to your dog's differing appearance of her eyes,
Found on a forum called the Naked Scientists:
I'll have a go at it...
Here's what we know. The tapetum lucidum, formed by the choroid at the back of the eye, is wedged between layers of blood vessels on either side but itself is avascular. It is responsible for reflecting light of various colours, producing the characteristic iridescence seen in flash photography of animals and in front of car headlights, and is believed to be a nocturnal adaptation by increasing stimulation of the photosensitive cells of the retina.
In dogs and cats, the tapetum is made up of cells. These cells contain crystalline rods that are arranged in such a way that they split the light that hits them into its various colour components. A similar effect is seen in herbivores, but the structure of the tapetum varies in that it is fibrous (collagenous) rather than cellular, and it is the arrangement of the collagen fibres within the structure that is responsible for splitting light. The tapetum is absent in humans and pigs.
So here's what I think might be happening:
1) The eye that appears red lacks a tapetum lucidum and the result is the typical 'red-eye' seen in humans due to the appearance of the blood vessels of choroid and the underlying the cornea.
2) The dog has different crystalline or cellular arrangements in its eyes causing the reflected light to correspond to the different wavelengths. Interestingly, tapetum appears a blue-green colour in the Dutch sheep dog but an orangy colour in the Old English sheepdog.
3) The dog is slightly bung eyed and light is hitting the structure at a slightly different angle in one eye than in the other, affecting the way the light is reflected (but being an appauling physicist, I have no idea whether or not that is valid.)
So, my guess would be that your dog has tapetum lucidum in one eye and not the other, or he has it in both eyes, but one of them is a "lazy eye" or angled slightly differently, so the shine does not occur at the same angle when viewed by you. (More probably the first).
Edit: I now realize that I never really answered your question. No, there is no worry due to the single eye shine. Your dog will be able to see a minor bit better in very low light in the eye with the shine, but it should not affect his overall health.