Common mistakes:
Forgetting to check connectivity: A graph can have all even degrees but be disconnected.
Confusing Euler and Hamiltonian: Euler = every edge once.
Hamiltonian = every vertex once. Different problems, different complexities.
Wrong handling of undirected edges: When using an edge , mark both directions as used.
Off-by-one in path length: An Euler path with edges visits vertices (with possible repeats).
Not handling multi-edges: Some problems have multiple edges between the same vertices. Track each edge separately.