Classic Inequality

Applying the AM-GM inequality, we have:

$(s-a)(s-b)(s-c)\le\left(\dfrac{s-a+s-b+s-c}{3}\right)^3=\dfrac{d^3}{27}$

Similarly, we have $(s-b)(s-c)(s-d)\le\dfrac{a^3}{27};(s-c)(s-d)(s-a)\le\dfrac{b^3}{27};(s-d)(s-a)(s-b)\le\dfrac{c^3}{27}$

Hence, $(s-a)^3(s-b)^3(s-c)^3(s-d)^3\le\dfrac{a^3b^3c^3d^3}{3^{12}}$ or $\dfrac{abcd}{(s-a)(s-b)(s-c)(s-d)}\ge 81$

So, the minimum value of $\dfrac{abcd}{(s-a)(s-b)(s-c)(s-d)}$ is $\boxed{81}$ .