We propose a neural event coreference model in which event coreference is jointly trained with five tasks: trigger detection, entity coreference, anaphoricity determination, realis detection, and argument extraction. To guide the learning of this complex model, we incorporate cross-task consistency constraints into the learning process as soft constraints via designing penalty functions. In addition, we propose the novel idea of viewing entity coreference and event coreference as a single coreference task, which we believe is a step towards a unified model of coreference resolution. The resulting model achieves state-of-the-art results on the KBP 2017 event coreference dataset.