My best friend!

[szybki]

I tried to focus on his nose, but the eyes are not in focus.
Should I have focused on the eyes?

 

[sm4him]

Yes. Generally speaking, if it HAS eyes, that's where the focus should be. People, dogs, cats, birds, insects--focus on the eyes.
Getting eyes AND nose in focus could be worth bonus points. Depending on what lens you're shooting with, and the distance to your subject, you may need to stop down a bit to get both in focus.