First, some may say this is a duplicate of What should one look for when buying a used lens?, but I see it more as an update or complement for modern lenses.
I'm interested in buying a used modern lens with Image Stabilization, etc. What would you check when buying it?
The mentioned question refers to many good ideas when buying old, manual, lenses, but fails to give any ideas on how to check autofocus correctness, IS, aperture automation, and probably some other things I can't think of.
The origin of this question is due to an ad where it says “Works fine except for short focal lengths, where the aperture fails”. Wow, you start thinking of all combinations you should try when buying it, and you realize you need several days just to test it all.
So the question should resume to:
In addition to everything mentioned in What should one look for when buying a used lens?:
How do you test autofocus? At how many focal lengths? Do you need to check at different apertures, or one is fine?
How do you check IS? Trying improperly slow speeds to check it's doing its job?
How do you check aperture control? Do you check it at different focal lengths?
What else would you look for?