I did my 7 block arvo commute and almost came off twice at intersections. I realise my bike is a racer and not entirely suited for town use... not to worry, made a deposit on a MTB on Saturday. No this is the scenario and please remember, in Australia, we drive on the correct side of the road ie the left.

Pull up at intersection with car behind me. Wait till car goes passed and then look left and right and left again. Because I've just had my knees replaced with Borg implants I can't stand up on the pedals to accelerate so I have to kinda push off. By this time another car is coming from my right and because I've got little control I turn left and go smack into the curb. Did this twice and I figure someone out there will have better technique. Easily done since I don't have any.

Are you riding clipless? What gearing are you starting off at? As far as the curb...maybe you should pull up next to it, so you can put your foot on the curb without actually dismounting your saddle?

Lower your gearing.
Slow down futher away from the stop line so you can observe from on the bike.
Position your bike further from the curb : are you making a nearside or farside turn?

Riding clipless, going straight ahead through the intersection. I've got the thing in low gear