Residual moisture from the ripe seed flows freely through a paper envelope as it evaporates from the seed heads or pods. However, you do want to pre-dry any wet seeds or green seed pods.
The process is very simple:
-Put semi-dry seeds and even seed heads into a paper envelope.
-Label it with the plant variety, date, and color of bloom if you save them separately.
-Fold the lip over once or twice and secure it with paper clips, staples or tape.
Envelopes standing on edge take up much less space than paper plates. You can dry dozens of varieties for months, or even store them this way. If you hybridize or do breeding experiments, you could save seeds from each fruit or bloom separately. If your cat knocks the envelopes over, they won't spill.
But how do you avoid risk of mold if you have a BIG bunch of WET seed heads?
As mentioned above, if you were not able to let seeds dry on the vine, you need to get them mostly air-dry before you can pour them in a heap into an envelope and forget about them. The interior of a big pile of seeds or seed heads will stay moist longer than the exterior of the heap. Humidity can't escape easily through a thick layer of plant parts the way it can through thin paper.
Green or wet seed heads and seed pods will grow mold at relative humidity (RH) above 85%. Seeds will lose viability rapidly at much above 50% RH. They will air-dry to safe levels much faster on plates or in envelopes if you break them up into small pieces, remove stems or chunks that were holding moisture, and make a shallow layer. For rapid initial drying, a thin layer has less risk of encouraging mold.
If you had to harvest damp seed heads, or if you have a big pile of wet watermelon seeds, pack them thinly between two coffee filters and wrap in a big towel or t-shirt. Place something heavy on top for a few hours. Unpack it, stir them, and press-dry again. That will remove most of the water before mold can develop. It should only take two or three days spread thinly in a dry room, or a week at 30-50% RH to get the seeds mostly-air-dry (dry enough to prevent mold) and put them partway to sleep. Paper envelopes will let them "breathe" from both sides and will wick water away, unlike a plastic-coated paper plate.
Spread them out into a thin layer and stir at least daily to get them mostly-air-dry (say 50-60% equivalent RH inside the seeds themselves). You can use a paper plate for this, or a big paper envelope.
Make sure you don't fill the envelope too full of green bits, or stack multiple envelopes pressed together. That would risk mold if the center goes above 85% RH.
Lay the envelope on its side after folding and paper-clipping it closed. Shake the envelope to spread the seeds out into a shallow layer so that they dry below 50% RH as soon as possible. I would remove the seeds from the seed heads or pods at this point or sooner.
When an envelope or piece of newsprint, paper towel, or coffee filter in contact with the seeds remains stiff instead of becoming limp from moisture, they are dry enough to pour in a big pile into an envelope for slow, long-term drying or storing without checking for mold.
If you have small batches of seeds, you can take up even less room by cutting envelopes in half "up the side," then folding and taping or stapling that edge.
If your indoor air is humid, you can speed up the last stage of drying with desiccants. Seeds stay viable longest if dried all the way down to 15%-30% equilibrium RH. The length of time that seeds stay viable approximately doubles for every 10% reduction in their equilibrium relative humidity.