Entering US w/ previous employer's Valid Visa (stamped) and new employer's transfer receipt

I need some expert advise or based out of real time experience-

  1. How safe/advisable it is to travel to US w/ a valid stamped H1 (in old passport) from previous employer and w/ the transfer receipt from new employer?

  2. What if some one overstayed by around 45 days in US based on the i-94 date specified in the passport during POE. There was some confusion as the i-94 date in approved i-797 petition was greater than the one specified in the passport. The one specified in the passport was based on the old passport expiry date and it was renewed in US itself (before the i-94 date mentioned in the old passport). Will there be any issues at POE? Can it be handled by explaining the officials about the situation?