A detailed transmission electron microscopy (TEM) examination of the surface of multi-walled carbon nanotubes (MWCNTs) oxidized using mild experimental conditions shows evidence of nanotube length shortening after acid treatments and important modifications at the nanostructural level, such as damage to the graphitic structure and stripping of the inner layers. It is shown that damage caused to the MWCNTs strongly depends on the acid concentration, even for short exposure times. Structural damage and fragmentation generated by a treatment based on 3.0 M HNO3 followed by H2O2 is mild compared to the severe damage caused by a combination of concentrated nitric and sulfuric acids.