Rodney is on the autism spectrum
The character tics (stimming, obviously), the varying niche interests, the lack of social skills, the apparently rather specific taste in food and drink, the difficulty with facial expressions, the odd speech patterns… all of this seems to point to Rodney being on the autism spectrum. Seeing Rodney's reaction to learning that his mother was murdered will be what finally convinces Karen that he's not the killer she thinks he is
How Karen will see it depends, though the likeliest scenario will be that she'll sneak over to his house again and start filming him right as Chad's finally breaking it to him what he learned about Rodney's mother. Rodney, contrary to Karen's expectations of him actually being the killer, will break down in Humanizing Tears, and this will prompt Karen to both finally realize she was wrong and have a My God, What Have I Done? moment.