D

To analyze the statements, let's break down each one based on the principles of dimensional analysis.

Step 1: **Evaluating Statement (i)**: A dimensionally correct equation may be correct.
This statement is true because a dimensionally correct equation that follows the laws of physics and empirical data is likely to be correct.

Step 2: **Evaluating Statement (ii)**: A dimensionally correct equation may be incorrect.
This is also true because a dimensionally correct equation can still be based on incorrect assumptions or approximations.

Step 3: **Evaluating Statement (iii)**: A dimensionally incorrect equation may be correct.
This statement is generally false, as an incorrect dimensional formulation usually indicates a fundamental flaw in the equation.

Step 4: **Evaluating Statement (iv)**: A dimensionally incorrect equation may be incorrect.
This statement is true because if the dimensions do not match, it implies that there is an underlying issue with the formulation of the equation, making it likely to be incorrect.

Thus, the correct selections are (i), (ii), and (iv).

Therefore, the correct answer is Option D: (i), (ii), and (iv) are correct.