Continuity mistake: When Neal is walking to the space where his rental car is supposed to be, he looks down as he walks past stalls V-2 and V-3, yet after V-3 he passes two more cars before arriving at stall V-5.
Continuity mistake: When Neal is scanning the parking spaces in the rental car lot, the shot switches to Neal's POV and back. When the camera is on Neal, he walks completely past the Mercury Sable in stall V-2, yet when it switches to his POV he's only just beginning to pass the same spot. As he approaches V-3 in the POV shot, the camera switches again and he's now well past it.
Continuity mistake: When Neal and Del are waiting for Owen in the Braidwood parking lot, a couple of the cars change type and position between the overhead shot when Neal says "Just get me to the train station" and when we see Owen's truck pulling up. There was not enough time between shots for any cars to have moved.
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