That's certainly an interesting idea, but it may prove a bit messy to give a reasonable implementation. In the default case, i.e., within the polar circles on days on which the Sun or Moon doesn't rise or set, it might be fairly straightforward. But in more special cases, e.g., at moderate latitudes on a day on which the Moon doesn't rise or set (there's one of each every month), results could be a bit confusing, especially if the user has specified something like 1-minute intervals for +/- 10 minutes on either side of the phenomenon that did not occur. Sun "rise" or "set" also may not occur at moderate latitudes if a nonzero altitude has been specified for rise or set; the greater the altitude, the further outside the polar circles this can happen.

At the very least, the suggestion to manually select 0:00 and 24:00 for the display of Sun and Moon positions when rise or set do not occur should probably be added to the Help page. You obviously figured out the solution, but it may not be obvious to everyone.

I recently found a couple of real bugs, though they won't affect most users:
  1. The latitude of Shanghai is wrong (it should be 31:14 rather than 39:14).
  2. Handling of an observer at a height greater than the surrounding terrain isn't always correct. If a nonzero Observer's Height and a nonzero rise/set altitude are both specified, the altitude is still adjusted for the observer's height--this should not happen. Furthermore, atmospheric refraction isn't included until the apparent altitude reaches zero. If an observer is substantially above the surrounding terrain, the Sun or Moon is visible at apparent altitudes less than zero, and the effect of refraction should be included. In most cases, this isn't an issue, but an observer watching the sunrise from Pikes Peak in Colorado can see the Sun at an apparent altitude of about -1.8 degrees.

These problems will be fixed in a future version. In the meantime, there are simple workarounds for two of the issues:
  1. If the location is Shanghai, select it, then click Copy Place, select Custom Location, and edit the latitude.
  2. For an elevated observer, either ensure that a nonzero rise/set altitude is not also specified, or if a nonzero rise is required, set Observer's Height to zero. Again, this is a pretty unusual situation.