Does vitamin b12 deficiency cause brain and nerve problems?

Yes: In the early 19th century, scientists noted weakness and numbness with B12 deficiency. Recently, B12 has been shown to upregulate neurotrophic factors (chemicals [cytokines] that help nerve cells grow) & downregulate neurotoxic factors (chemicals that break down nerve cells). In other words, B12 helps nerve cells grow and prevents their destruction by naturally occurring brain chemicals.

Yes: It can affect the spinal cord as well.