Method of derived class needs to downcast its parameter

Answer 1

It sounds like the Tracker class would best be a template instead of being derived from a common ancestor:

template<typename Element>
class Tracker {
public:
   void add(Element* p);
private:
   vector< Element* > vec;
};

typedef Tracker<Base> BaseTracker;
typedef Tracker<Derived> DerivedTracker;

You could then add a specialization of the add() method that uses Derived's special features:

template<>
void Tracker<Derived>::add(Derived* p) {
  p->spec();
  vec.push_back(p);
}