I will try first put in some history, and then try to address each common problem.
Windows DPI setting: Dots Per Inch (a dot is also referred to as a pixel).
Depending on the size and resolution of a screen every screen has a DPI.
Every object put on a screen was originally drawn using a given amount of pixels. If, on a given screen, that object is now too small you might "scale" it up, which is to say for every 1 pixel in the object use say 1.25, or 2 or some other number of pixels.
UPDATE! Quicken 2015/2016 now support Windows scaling (except in a few sections like the new Portfolio X-Ray, which doesn't scale. Note the X-Ray feature is only in the Premier and higher versions). Also another person has mentioned that the annual budget view isn't being scaled right, and the columns are too narrow cutting off some numbers. I just noticed that the system menu (File, Edit, ...) doesn't properly scale when selecting View -> Use Large Fonts (true of Quicken 2014 too). But it will respond to Windows scaling. This is based on me setting my screens to different settings, and from the feedback of another person that was using a Surface 3 Pro. Note on tablets you might have to use a mouse instead of the touch screen. Also on a Lenovo Yogo it has been mentioned that the Tax Planner is messed up.
MAJOR UPDATE!!! A Quicken user has found workaround for the problems people are having with high resolution screens.
Please see in the answer below.
Note there is currently a bug in Quicken 2014 R7/2015 R8/Quicken 2016 R4 that if you have multiple screens and they are set to different resolutions, and you put Quicken on the screen other than the primary screen it will mess up in maximized mode. It will have a big blank spot with the window data pushed to one side, as shown below. This is due to Quicken looking at the primary monitor to decide what size it should be in maximize mode.
A workaround is to make the screen that you are trying to display Quicken on, the primary/main display. Right click Desktop -> Screen Resolution, click display where you are going to display Quicken, and select Make this my main display -> OK. (Or of course you could run in non maximized mode).