How many side quests have I missed out on?
It's hard to say. You need to be talking to everyone and more than once too, because sometimes a side quest pops up from someone who had nothing much to say (or who wouldn't talk at all) the first time around.
Check out the Job Board, of course.
Most areas in the game will be visited twice if you're doing everything; some of them need to be visited a third time (the Wasted's to get the Quake room).
The sewers are good for mindless blasting and you get to pick up some valuable junk, as well as a nice reward second time through.
Look out for all the red, purple, etc plants. Some of these are well hidden away and they come in handy for recipes.
Do lots of races and pick up Sally's bounties as much as you can (take the odd trip out into the Wasteland just to blow away bandits, not even as part of a mission, for this) so that you can get vehicle upgrades; these come in very handy as you go through the game.
Search out the jumps and field goals.
All of these are available for doing well before you hit Dead City. Fortunately, you're not yet at a stage where they'll be locked out (not sure if they ever are) so you can come back and pick them up after you've done the City.