If he lived alone with his mother then the story of that being his childhood home also was a lie????...but,there was "Drew" written on a tree...on the other hand if it really was his place, pretty big house for a single mother and her only kid...
If he had carved 'Drew' when he was younger, then wouldnt it be higher in the tree? I dont' know if this is listed as a goof, sorry if it is, but you'd think the tree would've grown at least a bit in, what was it, ten or twenty years? Also, the family he lived with, for the girl to have known that park when she was 9 wouldve meant they lived in the same town... Why didnt they know each other if they lived in the same town when she was nine, and when he was a kid.
Up until the '70's it was very possible for lower middle-class people to own a house, many of them paid off within 10 years. It was in the 80's when my older sister bought a car for which she paid more than she and my bro-in-law paid for the first house they owned. I no longer remember what happened to Ben's dad--I had the impression he died in which case his insurance probably paid the mortgage. Even if they divorced, the mores of that time would have demanded that Ben's mom get the house. If he just "left," it would have been even more clear-cut.
As for Drew and Alicia living in the same town, and not knowing each other, that's not unusual. It would depend on the size of the town, and where Drew lived after he left the house. My parents grew up in the same town, and went to the same high school (just different years), and they never met until my father worked in an office after college graduation, and my mother was hired as his secretary.
One interpretation is that Drew's childhood home was in an apartment building which is now gone, so he hired an agent or a crew of agents to locate an idyllic fantasy home. The carving in the tree trunk looks to be of recent vintage, and the agent(s) may have smudged it with dye to give it a bit of an aged appearance. Of course, the problem with this theory is that little time elapsed between Drew's confrontation with the therapist and his arrival at the home; but, still, the scenario is possible. I do not mind ambiguities or plot holes, provided that the overall story has merit. I will take this movie over at least one other domestically-set Christmas movie which was of the same era and which was better received.