I'll second Howard's opinion. Also, it can't hurt to use a little extra caution in a few spots. Crossing the Ike, some of the expansion joints have lost their rubber gaskets, leaving gaps - good spot to slow down a little. Between Roosevelt and Canalport, new condo development means more parked cars and more traffic congestion - good area to watch out for dooring when you're in the bike lane.
... Halsted is "good" down to about Pershing (39th), OK down through the 4000s, and starts to get not so OK into and beyond the 5000s.
Not talking about automotive traffic or pavement.
I live in Bridgeport, so I take Halsted and Canal on a regular basis. I really like Roosevelt and Halsted, they have bike lanes most of the way and you don't have to worry about train tracks or potholes for the most part--a huge benefit if you've got skinny road tires.
Canal is alright as long as you're north of 18th Street.