When your website shows accurate and current information it helps build a level of trust for those potential customers that visit your website.
By displaying the correct copyright year it shows your visitors that you are updating your website on a regular basis. I've seen copyright dates from over 10 years ago on websites. To me if I see this it shows me that the business is not taking their information that they provide on their website seriously. I would have some doubts as to how on top of their game they would be for something as simple as updating the copyright once a year.
Just be aware of the little things. In the long run it might earn you new business because you were staying on top of things that mattered to someone who was noticing.