Your issue will be due to the Dashboard being set to Automatic resizing, especially since you developed on a larger size than on which you projected. If you'd developed on a smaller size than what you projected, you might have got away with it, but because it was the other way round, everything became squished (scrollbars, text cut off etc) because there just isn't the room to show everything you wanted. When re-sizing, Tableau does not adjust any font sizes, its just the various object containers that adjust. It is highly recommended that you always fix your dashboard sizes if you want to ensure you have no surprises when viewing on other devices, or at the very least, if you think you really what to go with automatic, then do what you can to check what it will display like before you formally present.
The help articles below will given you a few pointers.