Visible crew/equipment: When Neil exits from the airport just after the employer told him "You are f***ed", some onlookers and a crew member moving the camera on the dolly track can be seen reflected on the glass of the entrance from which Neil comes out.
Audio problem: As Neil is talking to his coworker about getting on a plane, the audio is either different or synced wrong, as the coworker says something different. In the shot facing Neil his mouth doesn't match.
Continuity mistake: After the train breaks down, the scene apparently takes place in the late afternoon. The sun angle is low in the shots where Del is hauling his trunk across the field. We then see a wide shot and the sun is higher in the sky.
Continuity mistake: Neil returns to the station where he left Del at the end. As he gets off the train and goes into the station, it's not the same station he was at earlier. The background outside shows houses and trees. Where did the buildings of Chicago go?
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.
Factual error: In Wichita, when Del and Neal are getting picked up by Owen at the Braidwood Inn, there is a mountain right behind Owen. There are no mountains in Kansas.
Other mistake: When Neal checks his airline ticket it says he departs from N.Y.C. J.F.K. but the movie claims to have him flying out of LaGuardia.
Continuity mistake: After leaving the El Rancho hotel. (when pulled over by the state police) Neil seams to find some new clothes, including a too small hunting hat, and scarf. On the walk home, Neil is carrying a large suit case, instead of his garment bag and brief case.
Plot hole: After the car burns, and they arrive at the motel, Neal only has $17.00 on him and nothing but melted credit cards, forcing him to give up his watch to help pay for the room. Del only has $2.00 but his watch doesn't quite flip the bill. At this point, between Neal and Del, they only have $2.00. However, when Neal invites Del into the room, so he doesn't freeze to death, they are eating Doritos and drinking shooters. Even in 1987 Doritos and a bunch of shooters must have cost more than $2.00. This is assuming Del didn't already have them in his trunk. But even if he did, at the end, Neal gets on his train, makes a return trip to find Del just where he thought he'd be, and then they'd both have to get back onto that train. After all, they both showed up at Neal's home. Once again, It would take money to get on that train. Four train fares with only $2.00. Neal's first trip, return trip, and Neal with Del for the last trip = four fares.
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