I recently found that it is possible to create circular link relationships between tasks within the PWA Schedule Webpart. Project Pro checks for things like this as you are editing but the PWA webpart only calculates and checks for things such as circular logic when you hit the Calculate button. The part that makes it more difficult to deal with is that the error message that one gets when the Calculate action finds the circular logic does not contain the ID of the task(s) involved in the link the way that Pro does.
This means that if a user goes into the schedule webpart and makes many changes, including some circular logic they will not see the error message until they hit Calculate or Save, at which point the bad link is already in place and the error does not tell them which task it is.
The solution is to open the project into Pro which will immediately let you know about the bad logic and give you the task ID.
The error you see when you save or calculate is like the one below: