Certain NMR experiments offer clues to differentiate a signal from the main unknown and from the impurity(ies). Some clues are not as obvious as others and so it takes a little practice to understand what to look for in a dataset.
A 1H-1H double quantum filter (DQF) COSY experiment (shown below) is used to filter out uncoupled systems. The alleged impurity singlets at 1.68 and 2.14 ppm do not show any diagonal and off-diagonal correlations. As such, this 2D NMR experiment is a bad choice in cases where the impurities exhibit uncoupled proton signals.