The area of the metal plate is $42\text{ cm} \times 14\text{ cm} = 588\text{ cm}^2$. Each small square has an area of $(7\text{ mm})^2 = 49\text{ mm}^2 = 0.49\text{ cm}^2$. Therefore, the number of squares is $\dfrac{588\text{ cm}^2}{0.49\text{ cm}^2} = \boxed{1200}$.