Would laser eye surgery help improve the eyesight of somebody with a nystagmus problem?

Possibly not: If the lowered vision is in part due to a refractive error, than lasik will improve that portion of the vision. So if glasses help the vision, then lasik will help to that degree. If the lowered vision is from nystagmus, lasik will not alter that eye movement and the vision will remained lowered. It is a combination of the two. Also, if the nystagmus is not controlled, lasik can't be done.

Possibly: If the patient is able to be refracted, and vision improves, then laser surgery could improve someone that has nystagmus. (there are some diseases where permanent poor vision and nystagmus is part of a syndrome.) now, trying to do laser on someone's who's eye is in constant movement.....Good luck with that!