After Monica pulls her hat off while washing Pete's feet, the shots of her face show her hair messed up on the top of her head. When the camera is behind her, her hair is combed perfectly.
Monica and Tess created an entire house for the Thanksgiving show, so it makes no sense for Monica to be begging for a place to sleep.
Having 3 famous celebrities guest star as homeless people just does not work. They should have been unknown actors or been cast in different parts.