I set off to play the Adventure in co-op mode on my local network, however the quantity of bugs is becoming a bit overwhelming.  So far, I've run into random disconnects, clients closing without warning, etc.  Anyone else had similar experiences?  Any advice?  I'm loving the game, but I'd love it more in co-op...

perhaps you'd have more luck online? it's seemed alright to me so far

I actually seem to have started this topic in haste.  After today's patch, we've gotten through a couple of chapters with only mildly inconvenient bugs instead of game-breaking ones. 
 
I think it'll be interesting to see how the online community develops around this game... even playing with just one other person, I seem to run a fairly good change of scorching, zapping, or otherwise dooming my partner...

Luckily patches come out almost every single day to clear the holes. I believe they're focussing on the online content first now.

The only bug I encountered when I played online with a friend was that the one that joined the server owner couldn't see the subtitles and with everyone talking like the Swedish Chef... well that's a gamebreaker to me.
No idea if they've fixed it yet though, haven't cooped since last week.