Revealing mistake: Near the end of the film, when Neal is on the final L train home, we see the train pull away from the station. When Neal returns to the station to find Del, the footage of the train leaving is played backwards - you can briefly see a man walking backwards at the top left of the screen.
Revealing mistake: When the couple is yelling to Del "you're going to kill someone" because he's driving on the wrong side of the interstate, you can see that their car's transmission is in PARK. (00:59:35 - 01:01:05)
Revealing mistake: When Steve Martin first calls home to tell his wife that the flight is delayed we see a lovely, cozy picture of the Page family enjoying a delicious, home cooked meal. However, in the shot where the kids are all sitting at the table the youngest child (back to camera) is being carefully 'watched' by a woman who is sitting on the floor next to his chair. I presume it is the actor's mother making sure that her little baby doesn't fall off the chair...
Revealing mistake: When they are sitting in the bus station in Jefferson City - and then the next scene is the somewhat "speeded up" shot of the kid running up and down the aisles of the bus (before the "take a picture, it'll last longer" scene) - as the kid is running up and down the aisle, watch the woman in the front left seat. The handheld windmill that the kid is running with hits her in the head and her eyes "pop open" as to be surprised by the hit.
Answer: He's not homeless, he has a house or an apartment somewhere, or lives out of hotels. He just no longer has a 'home', ie, a place where he's happy and someone loves him.
Brian Katcher