I have a confirmed electronic air ticket to visit USA and Canada which is confirmed with my old passport. But I have obtained a new passport for USA visit. Will there be any problems when I will check in at the airport counter?
No, the passport and Advance Passenger Information merely need to be correct at the time you check in. You can update the information at check in, either online or at the desk.
Remember that, if you are a visa waiver national travelling under an ESTA, you will need a fresh ESTA with each new passport you use to enter the United States. If you have been approved before it usually processes within one minute.