You can use any Video Editing Software e.g Adobe Premier Pro, you can see frame by frame, if the frames contained Double-lined, Shaky Motion-blur frames, then Stablize it as you say. You can use Sharpen on Mask Layers on top of Video to see, because you can see shaky after Sharpen. Or you can see the shaky by mute your audio, and Make it Slow Motion for while, remember to change it back to normal speed.
In fact that you have to find where's shaky by your own manually. Because this year still haven't come out Auto-Detect Shaky Video Plugin or Software. But, it is already has Plugin for perfect shaky detection & Stablize Plugin here. You can find more Perfect plugin for you video editing software.
Only a Programmer, can let Python Script in software help them auto-detect it. Here's Script But, the video will broke if you use that scripting.
The best option to avoid Shaky Video is Buy a Video Stablizer, it is a tool for stable video.