Classification is not the problem, overall due than the number of invert species kept at zoos are quite small compared to vertebrates. Most zoos shows basically the same species of stick insects and tarantulas, butterfly houses usually have the same few species of butterflies, and similar thing happens with marine inverts. The real problem would be: most species (well, large crustaceans are an exception) are very short-lived, and the interest of general public as well as zoo staff is much littler than with larger animals, so most zoos don't keep updated their list of invertebrates or ever don't put signs to them... so if a single zoo in most cases make some gaps with them or forget them (for the mentioned reasons of short lifespan and little public interest), what a nightmare would be the conjunct of all european zoos???