After Mike and the boys bring the Christmas tree into the house through the front doors, Mike closes the right-side door but leaves the left-side door open. A moment later, after Mike carries the tree to the entry landing, both front doors are closed.
While in the department store to visit Santa with Cindy, Mr. Brady tells her that he has to excuse himself to return a Christmas gift, the neatly wrapped package under his arm. There is no logic to returning a package that is still neatly wrapped: you wouldn't know what it is, why you needed to return it and the department store would not accept the return of a wrapped piece of merchandise. Finally, since Cindy came to visit Santa, it is apparent Christmas has not even arrived yet. EDIT: Mike had already told Alice that he would return the tape recorder due to Carol losing her voice, even though the tape recorder would be useful after Carol's voice had healed. He likely kept it wrapped to avoid alerting Cindy about the tape recorder and upsetting her more.
Carol carries the vaporizer with her into the living room while Mike and the boys are trying to place the Christmas tree. It's obviously an AC unit and unplugged, but when the camera focuses on her, water vapor can be seen emitting from the vaporizer.
When the boys bring the Christmas tree home its never explained HOW they got the tree home.