Carbon nanostructures are synthesized using a novel arc-discharge in solution process. A multitude of defects on nanotubes and nanostructures is found. Evidence of these defects in as-synthesized carbon nanostructures is explored using high-resolution transmission electron microscopy (HRTEM). Tri-, tetra-, penta-, hexa-, heptagonal, toroidal, oval, and spherical nanoshells are found in HRTEM investigation along with carbon nanotubes, carbon nanohorns, carbon rods, nanoporous carbon, dislodged graphene sheets, and amorphous carbon. Purifications are carried out through two oxidation methods to eliminate the amorphous carbon. Several different defects caused by oxidations are also found in purified samples.