Recently finished Balkans '41 and just started France '14 and have a couple of questions with respect to fortified zones placed ON river lines;
1) Do you suffer any penalty for being dug in on the river line or do you just lose the attacker penalty that could be gained if you were behind the river?
2) if you blow a bridge in/under the fort do your defenders suffer supply wise?
I know I can/could find the answers in the manual / on the net but I thought if we discussed it here we all might learn something.

I'll give you my thoughts on how I think it's supposed to work according to the manual, and I know that during the upgrade a lot of testing was done to make the manual accurate, but I haven't tested all this myself in TOAW III.
I'm not aware of any penalty for being dug in on the river line; but you would lose benefit of the .7 multiplier that would apply to the attacker, if you were behind the river, and since those two should be cumulative, you'd be better off digging in behind the river, rather than on it.
On the second question, I've noticed different results. In COW (and I assume in TOAW III) supplies could not pass over a super river/ super canal, unless the bridge was up, or a major fording unit was in place, or a unit with engineers (trying to build a bridge where there is a destroyed bridge). This affects your units on the opposite side of the river, from your supply source. But I've also noticed that often the river hexes themselves don't seem to suffer, they seem to have full supply. I don't know whether this is because of the terrain in the river hex, being close enough to a supply source or rail; or whether it's because the program is recognizing a blown bridge, as a good road. Or whether they're only supplied when you have a unit sitting on them, because a unit's presence does always seem to permit supplies to flow into that hex.
See also my post of 2-21-04 in the thread, "Supply Questions"; but again, those observations were tested in COW, not TOAW III.
Thanks Ed
That is/was my reading of the situation too, one of the things I like about the TOAW system is that when I feel instinctively about something by and large it seems to work that way in the game.