Two main issues that end up being great for us when trying to surface functionalize carbon nanotubes.
1. Surface functionalization always modifies the electronic properties of the material, complicating the characterization. But! This is awesome for sensors because if you can modify conductivity of CNTs by adsorbing molecules on them, they would make an excellent base for a sensor.
2. Issue with the relative inertness of the sp2 bonded graphene sheets that comprise the nanotubes. The curvature of the nanotube puts a relative strain on the sp2 bonds - the ideal geometry would be planar for sp2 carbon. But! This strain increases their reactivity due to increased surface energy.