I have to click the continue button twice

It happens when the continue button loses focus and it's possible in accessible courses.

If the quiz template variable HighlightQuestionIfAcessible=yes (or blank as 'yes' is default value) then quiz after pressing the submit button sets focus to the feedback text (in order to screen reader can immediately read it).

In this case the continue button loses focus and first mouse click will set focus then second will press the button.

Set HighlightQuestionIfAcessible to no and this button will not lose focus.