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I am doing a viability test on some old heirloom seeds I found (were my late fathers, so wanted to give them a go for sentimental reasons as they were ones from him/his garden)
I put them on damp kitchen paper and covered over with thick towel and put in warm room ( so dark/warm)

Some are swelling nicely and look ok, a couple have start of blue mold on the area where sprout would come. Is this time to discard those or keep watching?

ps. I only have 3/4 of some of them, so that's why I am trying to conserve if possible, rather than chucking!

suggest separate the good from the possibles and treat it as a further test would have thought the whole process would be doubtfull if the seeds were older than five years 

If they rot, pick them out. If you keep going, you may well find some that germinate, and you only need a few to start with, as it's easy to save your own seed for next year.