I relocated to another state and filed with the correct address last year. My employer however did not update to my new address. Will that cause a problem with IRS?

The IRS knows that people move all the time.   Just make sure that the address you use on your tax return is the address you want the IRS to use if they need to send you a letter or a check.

As for the state----you may have issues regarding which state they employer withheld tax for.  What are the two states involved?