The ostracodes are really small and delicate. Look for the sweeping extinction and look for the delicate arch shape of the shell and in well preserved samples one can see a hook or hinge where the two halves of the shell joined. Trilobites are much larger than the ostracodes. The sweeping extinction is very pronounced. Barnacles are much more complex in their shape and do not always have a well-developed sweeping extinction.
Corals present some challenges.
Paleozoic forms secreted calcite whereas the Cenozoic forms produced aragonite. Next the chamber wall is characteristic. In well preserved specimens look for crystals whose long axis is normal to the wall or septa. Be prepared to miss identify these as bryozoa and visa-versa. Bryozoan identification can present a challenge as they could be easily confused with a coral or when fragmental with that of a brachiopod.