it depends on the following techniques you'll use after PCR, since these mismatches can affect the productivity. why don't you prefer designing primers specific to the samples and verify if they are really specific? after all, you can mix them.
I agree with Frederic Lepretre that a mix of primers at the degeneracy or specific primers are best but in answer to your specific question it depends a lot on where the mismatch is situated on the primer. 3' and near 3' mismatches usually mean the primer will not work but many bases at or near the 5' end of a primer make no difference. Mismatches in the middle of the primer can be dealt with by making the primer longer to keep the annealing temperature high as the mismatch cannot be included in the annealing temperature calculation. 3' sequence homology is the most important factor in primers.
I may have misunderstood your question. If you want to amplify specifically in the presence of a very similar sequence then just a one base mismatch at the3' or 3'-1 position should be enough to only amplify only your primer in the presence of a similar sequence but great care on the annealing temperature will be needed.This is the basis of ARMS pcr and it does work well