The iron used in old boats was wrought iron, not the more familiar cast iron produced today. Wrought iron comes out of the furnace as a pasty lump which has to be well hammered with a trip hammer to drive out the impurities and condense the lump. It's this working that gives it the ability to withstand corrosion. If you see and old anchor that looks like it's rusting in layers, that's wrought iron. The layers are from the folding of the raw lump during hammering.
Wrought iron was never made into screws, instead it was formed into boat nails or rod. The boat nails I'm referring to are not the familiar ring shank nails, but instead nails sheared off a sheet of iron. The would have a square or rectangular cross section, a small head formed by upsetting, and a swelled section midway along their length. The were never bored for plugs, but instead driven in and set below the surface, the hole being filled with putty. Sometimes they went right through plank and frame and bent over on the inside.
Apart from the disintegration of the fasteners a bigger problem is the iron sickness of the wood, there's no permanent cure apart from replacement of the piece. As the iron rusts it expands, opening up the wood making little rot pockets all over. Oak is particularly susceptible to iron sickness, pitch pine much less so.
Anyway, I think most of this is somewhat correct, I hope it's helpful, and I welcome any corrections or further information on the topic.
Here's a good example of an iron sick boat fastened with boat nails. She's seventy years old here and way past her useful life, repaired many times and held together by force of habit. The cypress planks are not too bad, considering, but the white oak has been demolished by iron sickness, not rot. Most of the frame was pitch pine which held up rather well.
