Luckily you can do something about it:

• Use a different Render > Display Mode other than New Window. You should be fine using Full Screen, Image Editor and Keep User Interface.
• To work with different windows open: Set Render > Display Mode to Keep User Interface, and manually create additional windows from the menu Window > New Window. On your next renders, the slots will continue to be updated in all available Windows and Image Editors open.

Yes. Sadly, for version 1.0 of Shift Render Slot, there's a problem when Blender has to create a new window for the next render, causing it to freeze and making it to show the new window totally blank. This leads an unresponsive state of the program. This problem was fixed for Blender 2.81, 2.82 and 2.83 in version 1.1 of Shift Render Slot.

If you need to use the version 1.0 with Blender 2.80, just be careful. Avoid using the Display Mode > New Window, and make sure to save your project before you do any test with this.

The bug has already been reported to Blender developers, but it's a low priority task for the Blender Foundation and it isn't clear when will it be fixed.