Test an LCD for missing segments without looking at the screen?
You could produce an automated display monitor using OpenCV, and any computer you have sitting around which can handle the processing load. The trick is the camera. It needs to be high resolution enough to resolve whatever error you're looking for. 

In professional display testing environments very high resolution and finely calibrated cameras called colorimeters are used to test displays and evaluate their performance in conjunction with other tools such as spectrophotometers and other tools.

For your application, make sure whatever camera you use can clearly resolve the segments. You can write a program using OpenCV to detect and log the error. Depending on the resolution you're capturing and how fast you need to process a very small computer like a raspberry pi can handle the load.