To the best of my knowledge when the gun is battery, it shouldn't not wiggle much if at all. When the slide is locked back, it will wiggle quite a bit. The only weapons that do not wiggle when open is a blowback design where the barrel is fixed to the frame.
Yes 1911's are not fixed barrels, Whith the slide back the barrel will wigle a bit. I own and have built several (my wife says too many) 1911's. I carry one as my duty weapon and carry one as my off duty weapon. If it is a extreme wiggle or he is very worried about it take it to a competent gun smith.