When dealing with enzymes, a 1% impurity can either be nothing to worry about or can completely mess things up. If you mutate a key residue in an enzyme that knocks activity down by four orders of magnitude, but you have a 1% impurity of wild-type enzyme, your estimate of the effect of the mutation on rate will be in error by 100-fold. The same impurity in a crystallization experiment would probably have no discernible effect.
I can think of two kinds of impurities in commercial peptides, namely small molecules left over from the process of making/cleaving/deprotecting it, and other peptides (for example shorter peptides created when the coupling of one amino acid did not go to 100% completion. Small molecules can fluoresce, and this problem made one batch of peptide we bought near worthless in fluorescence-based titrations. The other peptides might or might not have the same biological activity as the desired peptide.