New password results in endless loop of Apple ID and device password?

I created a new log-on password for my iMac--what should be a straightforward and common operation. I also have an iPhone and iPad. Now every time I log on to a different device, it asks me for my apple ID and device password, and sometimes the password for other devices. Once I finish entering several passwords on one device, that creates the need to enter several passwords when I log on to another device, and so on endlessly back and forth between devices. I assume this is a bug. Or maybe there is a fix. Where can I complain to the software developers?