As for the slums, either down the river or on the side closest to the swamps (smell, vermine, fog... ambiance). We can have both, the city is big enough. The one downriver being merely poor, the other being poor and nasty. 
The bridges: I'm waiting a bit for those as I'd like to have the districts sorted out first. I think Jolly was willing to tackle that.
I'd sure like to make a contribution, Grey One...
BTW, great job with the map! Must be a lot of work doing it with good old 'Paint'.
I'm still on the tossing-around-ideas stage, mind you, but here are my thoughts so far:
Slums: As you said, the city's certainly big enough to have two of them, and placing one near the swamps and one downstream makes a lot of sence. Can't remember who came up with it, but I love the name "The Squats"!
The homes of the truely wealthy would logically be located upstream, where the river and air is the cleanest, and obviously away from the swamp.
The houses of the city's old families would most likely be somewhere in the middle of the city. This would be 'the old town', probably looking a little different from the newer districts that sprung up around it as the city expanded in all directions.
The government district could either be a part of the old town, or the city's growth could mean there has been need for more/bigger/better/newer houses of goverment, in which case they'd be somewhere on the outskirts of town with the more resent buildings. (Oops, just remembered your Island of Towers! Perfect location for a 'Old Town'-type goverment district!)
Harbors will obviously be very important to a city with a location like this. Trade ships are likely at least as common as caravans. Every little stretch of riverbank inside the city walls probably has a distincively 'harbor' feel to it.
However, I feel some locations should be even more clearly harbor district than the rest. There should be a dock somewhere upstream that's mainly for riverboats going between Mor's End and the Kul Moren mines.
The biggest harbor would most likely be along the biggest (western) river outlet, just up from the squats. This part of the city would have a lot of big warehouses and winches along the banks, for loading and unloading ships.
A bit further into the city (but not too far!) there would be a number of smaller docks for fishing boats. The fishermen was there before the traders, and so their docks would be closer to the original townsite.
A city this big would also need a wharf or two (or three!). These take up a lot of land, but isn't very fuzzy, so I guess the wharfowners would go for the less expensive plots downstream. I think along the southern fork of the river would be good a location for them.
Finally, I must admit to having a bit of crush on the notion of a small harbor district where the docks are built specifically for the smaller ships and boats of halflings and gnomes. Imagine all the little halfling inns, with their wonderful cooks, performers and pick pockets!
I'll be making a gnome NPC ships merchant, that would fit perfectly in such a location; a seller of ships rations, fishing nets, tools, rope etc. But also strange and wonderful devices he makes in his toolshed after closing time...
Gotta go now, but I'll be back after some hard thinking and sleeping!
