Alan should have wondered how Dempsey found out about the cheating.
He should have found out if Dempsey went looking for phone records.
Another thing was that he should have quickly moved and checked to see for that globe thing at his house.
Well to all intents and purposes the cops didn't really need to find out how Dempsey knew, he was claiming self defense and 'supposedly' learned about their affair after the attempt to kill him. In reality he knew due to the phone bills which showed his brother checking his messages from his house in the middle of the night. This would have been a better twist (also showing that Alan was just as good a detective as Dempsey) if Allan had found that call on the phone bill and asked how he had not noticed this...
As for the globe paperweight, he was hoping to trip up Dempsey with this wasn't expecting two of them, the second of which Dempsey claimed was under the sofa (which Dempsey knew Alan would not have had photographed).
When you talk to God it’s called prayer...when God talks to you it’s called schizophrenia...