What is the difference between ∀ and Π in the Calculus of Constructions?
I had only a quick and cursory look at the paper — so take this with great care.

It appears that $\Pi X$ is used to express dependent products as in the calculus of constructions. Instead, $\forall X$ looks more like polymorphic types in ML.

The main difference is that, if $t : \Pi x. P(x)$ then $t T : P(T)$, while if $t : \forall x. P(x)$ then $t : P(T)$. Note that the former requires an additional argument, the second does not: the polytype gets instantiated automatically. Rules $\mathit{App}$ and $\mathit{Inst}$ at page 7 cause this difference.

Of course, this also means that introducing $\Pi$ requires a lambda, while introducing $\forall$ does not.

There also is some type / kind distinction related to this, but I can't comment on that precisely.