Using "var" when creating new Person instances?

The use of var is optional though highly recommended when doing anything beyond the most simple script. The MSDN documentation gives a pretty good explanation:

Use the var statement to declare variables. You can assign values to the variables when you declare them or later in your script.

A variable is declared the first time it appears in your script.

You can declare a variable without using the var keyword and assign a value to it. This is known as an implicit declaration, and it is not recommended. An implicit declaration gives the variable global scope. When you declare a variable at the procedure level, though, you typically do not want it to have global scope. To avoid giving the variable global scope, you must use the var keyword in your variable declaration.

In the example Jim Hoskins was using in the video this doesn't really matter all that much but you're right, using var is a good habit to be in.