How to play 24 fps video smoothly on a 60Hz display?

Check out SmoothVideo Project:

SVP allows you to watch any video on your PC file with frame interpolation (like you can watch it on high-end TVs and projectors). It increases frame rate by generating intermediate animation frames between existing ones to produce very smooth, fluid and clear motion. The technology is well-known for a while ("TrimensionDNM", "Motion Plus", "Motionflow" and others), but now it's available for free to PC users with simple GUI and just a couple of mouse clicks.

I don't know of a player that can do that on the fly, but you can convert any video of 24/25fps into a nice 60fps video by re-encoding the video with interframing.

here is a very nice step by step tutorial to do it. It includes before/after video samples. http://www.spirton.com/convert-videos-to-60fps/

Your idea for making video playback smoother by means of what you call linear interpolation is simply a blend method of frame rate conversion (or Blend FRC). MediaPlayer.NET (MPDN) employs this technique and calls it "Fluid Motion". madVR calls it "Smooth Motion".

This method of FRC is the most basic of what SVP uses. However, both MPDN and madVR have the ability to detect the actual display refresh rate to a very high precision. While it is unlikely that you'll notice a dropped / repeated frame at 60Hz, SVP still suffers from the (however slight) mismatch of input / output rate (e.g. 60.001Hz+Reference Clock Deviation vs 60FPS). Using SVP is also a lot more GPU intensive than the player's blend FRC which costs only a fraction of render time.

If you're able to overclock your display, MPDN's rate tuner gives you an alternative to blend FRC and is generally considered the better option. Blend FRC can cause blurring / ghosting so it should be taken as the last resort. See MPDN rate tuner wiki on GitHub for more info.

Disclaimer: I'm the author of MPDN.