Big things are happening on TV Tropes! New admins, new designs, fewer ads, mobile versions, beta testing opportunities, thematic discovery engine, fun trope tools and toys, and much more - Learn how to help here and discuss here.
Before she left, Christine directed a woman and her daughter to check on the child. Speaking with them would at least have established whether Walter was taken early in the morning or later.
Since part of the point of the movie is that the LAPD is clearly not committing itself towards investigating and solving this matter with particular diligence, it's likely they simply didn't bother to speak to the woman and daughter in question.