If driver license address and filing address are different, would that be a problem for tax return? Does IRS check if both addresses match to verify taxpayer' identity?

No, that will not be a problem. The IRS uses your Social Security Number and the address on your return as your most updated address. 

Your driver's license is not required in order to file your taxes, for most states, but could help speed up the processing of your return and will not affect your return’s submission. 

In an effort to help protect your identity and fight tax Fraud, the IRS and State tax offices are now asking that tax filers provide their driver’s license or state issued ID number. 

States such as Illinois and Alabama do require an ID to be provided in order to e-file this year.

For additional information, you can view the IRS information on the New Security Safeguards. or to see if your state is participating, please contact your state revenue agency.

I changed my state ID address today to my house address. Won't make a difference???

No, that is not going to matter.   The address on your state ID is not used or asked for.   @Yep2

Drivers license is used for ID when filing electronically. The different state license will not be a problem?

The feds don't care what address is on the ID ... you don't even need the ID to file a fed return  ... however  your state may take issue.