For NMR, as with other spectroscopic techniques, spectra for impurities are easliy lost in complex spectra when the impurities are present at low level. When you use GC-MS or LIC-MS, you add a separation so the contaminant can be separated from the compund for which you are checking purity.
NMR gives a measure of everything in the NMR tube that has a specific type of atom, such as hydrogen, C13, etc. The mass spectrometer gives a measure of molecules that can be ionized to form a detectable ion, and when attached to a chromatographic instrument, is limited to only those moleuces that can pass through the chromatographic column and form a peak.