Cartridge new or used ?

First you have to know which stylus profile, then you can search for the manual to find out a life span of the stylus. Some of them must be replaced after 300-500 hrs, some more expensive can be replaced after 1500 or even 2000 hrs. You can count an average listening session at home, so you can imagine how long you can use a cartridge if it’s lightly used demo or hardly used cartridge.

With a macro lens you can see the diamond, but you can’t understand anything about hrs of use anyway. All you can see is that the diamond is sharp and not damaged. If you want to know more you can send a cartridge for inspection under microscope (to professionals), it will cost about $60

Personally i'd like to compare any unknown sample to my own sample. It's easy if it's the same cartridge, but the one i bought NOS (and when i'm the first owner). Comparing one sample to another will tell you more about quality of the used one. If the sound is not at good as another sample then the stylus is worn. 

You need an inverted microscope with at least a 40X or higher power objective in order to see the stylus shape and wear. The diamond should never be "sharp;" that would permanently damage a record. The profile needs to be smooth and polished, otherwise, if it has sharp facets due to damage, it will act as a lathe and will scour and scrape off the undulations in the vinyl.

Personally, I never buy used cartridges. Too much risk. It's not worth it.

This is MicroLine diamond under professional microscope and this is the same diamond under macro lens for iPhone. When the diamond (stylus tip) is bigger we can see the diamond much better, this is brand new, never used Dynavector MicroReach diamond, all we can see is a sharpness of the unused diamond. This is what i mean @stevecham  

Here is another example of the MicroReach diamond on the unused Dynavector 23RS cartridge. It is also looks sharp, but it's brand new. 

And finally Replican 100 diamond (the most complicated stylus profile ever) on very lightly used Ortofon SPU Royal G mkII. 

All pictures taken on my macro lens. Diamond in perfect condition or brand new diamond looks sharp. 

Damaged or worn diamond looks different, but to inspect them we need a powerfull microscope, this is an image from the internet, the diamond is worn accodring to the poster.