If your new 4K display is randomly exhibiting any of these issues, the first thing to do is try a new, DisplayPort-certified cable.
HDMI is trickier: While some 4K monitors support HDMI, the version of HDMI supported by most graphics cards — HDMI 1.4 — locks 4K output at a choppy 30Hz. The newer HDMI 2.0 spec supports a full 60Hz at 4K resolution, assuming both your monitor and your graphics card support it. Nvidia's new 900-series graphics cards support HDMI 2.0. In general, however, it's easier to drive a 4K monitor using a DisplayPort connection at this time.
The pixel density of virtually all of the 4K PC displays currently available is so high — because the pixels are so small — that icons and text can look incredibly tiny when 100% scaling is used. Raising the DPI scaling in Windows can increase the size of application windows and menus to make them more easily readable/usable. Not all applications scale properly when the DPI scaling level is increased: Some applications will look blurry, while others remain tiny, or don't render all interface elements properly.
Microsoft has focused considerable effort to fix scaling issues with Windows, and has also pushed software developers to fix their applications, but issues persist to this day.
Before getting a 4K display, do your homework. Check whether any of your most commonly used applications have problems on high-dpi displays. PCWorld's guide to making the Windows desktop look good on high-resolution displays can help you squash those pesky scaling issues if you decide to take the 4K plunge.
Sign up for Computerworld eNewsletters.