There are a couple of mechanics that can only be observed on a fully visible board (the death screen), such as the purple slime mage who is level 1 but is always surrounded by level 8 tiles or the basilisk that marks number tiles with a ? in a diamond shape.

Minor correction: it's a beholder, not a basilisk. Look them up, they're adorable.

One pattern is that all the 8s are always clustered around a single edge space that contains a level 1 wizard thing. I don't know if there are other patterns, none popped up immediately.

Rats always look at their king.

Other than what sibling comments said, the 11-strength enemy that drops the powerup to kill all mines is always in a corner of the board.