We introduce a general framework for several information extraction tasks that share span representations using dynamically constructed span graphs. The graphs are dynamically constructed by selecting the most confident entity spans and linking these nodes with confidence-weighted relation types and coreferences. The dynamic span graph allow coreference and relation type confidences to propagate through the graph to iteratively refine the span representations. This is unlike previous multi-task frameworks for information extraction in which the only interaction between tasks is in the shared first-layer LSTM. Our framework significantly outperforms state-of-the-art on multiple information extraction tasks across multiple datasets reflecting different domains. We further observe that the span enumeration approach is good at detecting nested span entities, with significant F1 score improvement on the ACE dataset.