Common mistakes:
Confusing Euler and Hamiltonian: One is polynomial, one is exponential. Double-check which one the problem asks for.
Missing the SCC step: If you need to do DP on a directed graph with cycles, condense to DAG first.
Wrong flow model: Not every optimization is max flow. Check if capacities and conservation laws apply.
Overcomplicating: Sometimes BFS or DFS is enough. Don't force advanced techniques.
Forgetting edge cases: Empty graphs, single nodes, disconnected components.
Step back and verify your model matches the problem.