How much trouble does it cause when you look different than your passport picture?

My husband is in the process of growing a beard. In his passport photo he is clean shaven. He has to go to China in January. I don’t think he’ll look significantly different, but he would like to avoid any hassles at security or customs.

Any insight jelly-friends?

NOTE: He will shave if he has to. We’re just wondering if there are any problems.