In the movie, Robin Williams friend was a make up/special effects guy who made him a smooth mask by first pressing and shaping this plasticy, rubbery substance on his face and essentially making a mold of his face so when he had it on, you couldnt see whiskers and such. Williams would carefully peel it off at night and keep it on a wig holder head and ready for the next day. I'm sure Joe have "people" who put his on for him and it looks like on this day they were in a hurry!