How can the chemo therapy drug vincristine be harmful?

Neurotoxicity: The major dose limiting toxicity of vincristine is neuropathy. There are other "usual" chemo side effects including bone marrow suppression -- lowering wbc, rbc, PLT -- but neurotoxicity is the one we watch for the most.

Neuropathic effects: Are most common with vincristine. Patients can experience pain, numbness, tingling (aka paresthesias), difficulty with chewing/jaw pain, foot drop and discoordination. Gabapentin and physical therapy may help wth these. Also a neuropathic complication, constipation is a significant concern since hard stools predispose to serious bacterial infection. Liver toxicity can be an issue also.