There is no single technique that will give you definite answers. NMR will tell you everything about soluble and proton containing contaminations. Elemental analysis, MS, (ie. ICP-MS, or HPLC-MS) can give you also additional information.

So the analysis and depends on the possible contaminations ...

Honestly speaking !!!!

NMR only give the proton and carbon environment of a compound. Although in respect to your question, i must to tell you that on the basis of single technique it really difficult to tell the purity of the compound. For structural, quantification and purity analysis, its always better to go for most basic technique...melting point. then..HPLC.....1H-NMR....13C NMR, MS and finally CHN analyser.

Sharp and blunt melting point will tell you the solidity and impurity level (only predictable in this case)...then HPLC will help you in purification. of your synthetics..1H-NMR and 13C-NMR will tell you the type and environment around the proton and carbon of your compound...which then ........further verified by mass via MS and lastly elementary analyser which will confirms the percentage of the elements in the compound.

So simply on the basis of one technique (NMR), its really injustice to say about the purity of compound.