The child that is driving Lily crazy in kindergarten is named "Johnny Marley". To punish him, Lily cuts the head off his stuffed horse, leaving it under his blanket at nap time. In the equivalent scene in the The Godfather (1972), the actor's name was John Marley.
The scene where Johnny wakes up with the head of his stuffed horse is a nod to The Godfather (1972).
The car alarm that Ted mimics to calm his class is the car alarm that Lily and Robin hear camping out for a wedding dress sale in 'Lucky Penny' (Season 2).
In The Godfather (1972) and its sequels, oranges are used to foreshadow a death or close call. As mentioned, Johnny waking up next to a horse's head is a reference to The Godfather (1972); in Johnny's first appearance when he's running around the classroom, he's holding an orange in his hand (which he drops).
First live appearance of Tugboat the dog. He previously appeared on a t-shirt.