This note investigates some decision problems for three-way two-dimensional finite automata. It is shown, for example, that (1) the emptiness problem for nondeterministic three-way two-dimensional finite automata over a one-letter alphabet is solvable, (2) the universe problem for deterministic three-way two-dimensional finite automata over a one-letter alphabet is solvable, and (3) the universe, containment, and equivalence problems for non-deterministic three-way two-dimensional finite automata are unsolvable.