Mice can squeeze through 1/2" gaps/holes. So even the tiniest opening can be an avenue in. I'd give it a real good look over for any obvious openings and less obvious ones, like loose boards.
Is that 1/2" hardware cloth? I assume the wood trim is screwed in over it? Should be good enough against most predators short of a bear.
What's the shed sitting on? Concrete pad or is it open to the ground? An apron would be advisable if it's sitting on the ground as rats and mice can dig...