I would think mice, or caterpillars.

EG

Are you seeing roundish holes with clean borders? Or does it look like little teeth have been munching on your greens?

Cabbage moths (those white butterflies you see flitting happily around the garden... the ones that I used to LOVE and now run around yelling at...) will lay eggs on your brassicas, which broccoli is, and sometimes lettuce (from what I've read) and then the resulting caterpillars will voraciously eat through your leaves. The holes start out very small, a little larger than a pinhole, when the caterpillars are about 1/2 a cm long, and will get increasingly larger as they eat and grow. If you see a fresh hole, look closely around it and see if you notice a green caterpillar around it. They blend in amazingly well, but once you know what you're looking for, you can spot them more easily. When they get out of control in my yard, my collards end up looking like someone ate all the leafy parts and just left the ribs.