how long to wait after reseeding to spray lawn?
Your herbicide's packaging will likely give instructions on this issue. It's best to wait as long as possible to apply herbicides to new seedlings as even though they are labeled for use on your type of turf, they are capable of weakening even healthy established lawns to a degree with every application. The rule about waiting till 2-3 mows is a good one.
If your lawn has had trouble looking good in the summer and really needed the seeding I would wait till next spring to give the new grass as much chance as possible to establish.
Broad leaf weeds are pretty easy to get rid of when the time is right. At at least they're green, not dirt. One of the big problems I find on customers' cool season type lawns is that the applicator has certainly removed most of the weeds but that the lawn's health itself is poor. Repeated applications can stunt the growth of the desired turf.
For best results, ALWAYS use a tank sprayer and spot-spray weeds, don't hose down the entire lawn with a hose-end sprayer unless it is really in terrible shape and you are aware of potential damage to desirable plants due to drift. It takes a little longer, and may require another go-round to hit spots you missed, but in the end you use a lot less herbicide, only hit areas that need it, and have a lot less chance of spraying trees and shrubs by accident.