Step 1: Check Statement I
$V_0 = \dfrac{hc}{e\lambda} - \dfrac{\phi}{e}$. When $\lambda$ decreases, $V_0$ increases, so Statement I is false.
Step 2: Check Statement II
$K_{max}$ has no dependence on intensity. Only the photocurrent depends on intensity, so Statement II is false.
Step 3: Conclusion
Since both are false, the option stating that both statements are incorrect is correct.
Final Answer:
Both statements fail, so the last option is correct.
\[ \boxed{\text{(D) }\text{Both the statements are incorrect.}} \]