In the opener, Doug and Carrie are sitting on the couch with a dog. The Heffernans do not own a dog.
As supervisor, Doug tells the drivers that because of road work on the Grand Central Parkway they should take the Van Wyck Expressway instead. Those instructions make no sense because delivery trucks are never allowed on the Grand Central Parkway so it is never an option for them.
When Arthur (Jerry Stiller) runs out of the house to the Good Humor Ice Cream truck, you can see that he stops at the porch. Immediately after, Doug (Kevin James) runs outside and you can still see Arthur standing still on the porch as Doug, supposedly calls after him running.
In one scene Deacon say to Doug that he's been working at IPS as long as Doug. However, in a flashback scene in another episode, that Deacon had already been working there when Doug started.