This paper presents a comprehensive analysis of directional derivatives and error bounds for the merit function θ(x)=supa∈ A(-ΔC(F(x)-F(a))) associated with the vector optimization problem MinC\F(x):x∈ A\, where ΔC is the oriented distance function. We first prove that θ is concave and Lipschitz continuous on the whole space and derive its dual representation via the weak^* compact convex set K=cow^*(S(C+)). At a weakly efficient solution x, we obtain the explicit formula θ'( x;d)=miny^*∈ W( x)⟨ y^*,F(d)⟩ with W(x)=\y^*∈ K:F^*y^*∈ -NA(x)\, characterize the zero-directional-derivative cone, and prove that, under a local error bound condition, the tangent cone to the solution set is TEw( x)=TA( x)∩ T\widehat A( x)=\d∈ TA( x):θ'( x;d)=0\. We establish the equivalence of thirteen distinct global error bound conditions, including characterizations via linear regularity, the global slope, an asymptotic condition, and perturbation stability. A central result shows that the global error bound property for θ on the feasible set A is characterized by a uniform negativity condition on the unit-sphere minimal directional derivative, namely supx ∈ A ∖ Ew φ(x) < 0. We also determine the optimal local error bound constant precisely as 1/φ( x) when φ( x)>0, and provide a counterexample demonstrating that an additional directional condition is essential when φ( x)=0. These results provide a complete bridge between the directional derivative of the merit function and the geometry of the solution set, offering fundamental tools for the convergence analysis of algorithms in vector optimization.