The most common cause of this is that multiple clients are attempting to connect to the broker using the same Client ID. In node-red the best thing is usually to leave the client id empty, then node-red will generate a unique id for you.
Also make sure in the MQTT nodes that you only have one broker config for each broker. When you click on the Server dropdown in the node you should only see one entry, unless you are accessing multiple brokers, in which case there should be one for each broker.