Hi Clueless (and you are obviously not clueless at all if you've discovered the joys of paper pots and made 400 of them!)
I use paper pots a lot - they are really good (although they do have a few limitations). So here is what I've found out after a few years of doing it.
1 - just water from the top as normal. You won't want your compost to be soaking wet for baby seedlings, so there isn't a problem with the pots collapsing (especially if you've got them nicely packed together in the seedtrays).
2 - yes they will go mouldy but that doesn't matter. You are going to plant them direct into the ground anyway, so if anything I think it is a good thing if they've started breaking down / rotting away a wee bit! Just as long as you don't get squeamish about mould...I've never seen the seedlings suffer from it.
3 - the compost does tend to dry out faster than with plastic pots - I guess it sweats away through the paper. So you do need to keep a close eye on your babies, and it is trickier to get the watering balance right. I've found that some of the more sensitive seeds (little fine ones for example) have not done well. But my sunflowers and tomatoes thrive. I'd suggest sowing more than you think you need, in anticipation of a higher rate of loss... (sorry)
4 - when you plant into the ground, especially if you've used very long strips of newspaper so there are lots of layers of paper in the pot, I think it is worth ripping them open a little to help the roots find their way out into the soil. You ought to see some roots growing through the paper by the time they are ready to go out; if you don't see any, then definitely do a bit of ripping open. This is especially true if you are planting in dry weather / dry soil; and it is one reason why I'm always quite pleased to see the pots beginning to get a bit mouldy and manky as they get closer to planting out time!
5 - I think that I've noticed that pages with shiny coloured paper (the magazines) break down more slowly and also that some seeds really don't like them. Maybe something about chemicals in the coloured ink? So if you've any pots that are particularly colourful / shiny, perhaps use them for the tougher babies (eg sunflowers, peas, beans...).
I think that's it! Let us know how you get on.