This is how I successfully reproduced the Nidalee spear bug (twice in a row! with VIDEO)
I reproduced this several times in an empty custom game (and a full of beginner bots custom game). I didn't record until I thought I could reproduce it easily and spent another 3 minutes until I reproduced the bug twice in a row.
What I did to do this bug: first thing I did was swap the attack move click to right click instead of shift-right click. Made things easier.
-I would mash right click (attack move click) and the "S" key (hold position) to try to get the wind up animation to just the right point -throw a spear at the very end of a wind up animation, when the attack has technically "left" Nidalee. -reissue the attack command -the auto attack will connect with the minion (or tower, which tends to be easier to reproduce the bug at simply because of the longevity of a tower) and as the missile from the auto attack disappears, so will the nidalee spear.
The timing window for this bug is INCREDIBLY narrow, but the spear from Nidalee's Q disappears when the projectile from her auto attack hits a minion and disappears. The times this bug successfully recreates, the spear from Nidalee's Q disappears as the auto attack damage is counted, but if you miss the timing on reproducing this bug you will not auto attack until well after you've thrown the spear. I think this bug's source is something to do with the client's disposal of projectiles.
EDIT: To reiterate, I used these steps to reproduce the bug several times before actually filming it. It is just extremely hard to hit the timing window to do it.
EDIT 2: as pointed out by BlackSunNocturne, it may also have something to do with one small fact: Nidalee's Q and Auto-Attack spears use the same model. It may be a bug with the coding the model. If one disappears, the other one disappears as well.