We have a sewer/sewer gas smell coming from a half bath and the connecting hall. The smell will occasionally go to our bedroom and master bath which is above the half bath and hallway. I had a plumber come in and he discovered that that the vents in these areas, including the laundry room, do not have air ducts that go all the way to the top opening of the vent, consequently there is about eight to ten inches of missing duct work. Could this be the culprit? Sometimes it seems like the smell is not coming directly from the vents.

We got some terms being mixed here. All drains need traps and a venyt stack. Vent stacks to to thr oof and above to allow air to move in and out of pipes when water drains, prevents siphoning of traps. There is no air duct with this, the vent is usually a 2" or bigger PVC pipe coming through the rook. If you have a gap, misssing section of vent stack there is your problem. Can't figure why the plumber did not explain this to you better and fix it