Common Mistakes

Mistake $1$: Forgetting that profiles represent which cells are already filled, not which cells are empty. If you invert the meaning, your transitions will be backwards. Mistake $2$: Not handling the base case correctly.

You must start with $dp[0][0] = 1$ (or the equivalent for your indexing). Starting with all zeros gives zero tilings. Mistake $3$: Off-by-one errors in bit indexing. Bit $i$ corresponds to row $i$, but if you're not consistent about $0$-indexed vs $1$-indexed, you'll set wrong bits. Test on small cases.