I know this thread is old, but I disassembled a BRZ transmission with 3-4 shift issues and 2 metal balls on the drain plug magnet.
I can confirm what AxisPower says in Post 29/31 - these are balls that fit into the syncro keys in the sliders. Without the springs/balls in-place, I don't think there is anything to push the keys into the syncro ring. Don't see how the syncros would function if all 3 were missing. Missing 1 would make it worse, but maybe still function. 2+ missing like this trans had...
In addition 2 of the springs had gotten snagged by something (the slider ?) and were bent/elongated enough to stick above the hole drilled in the key and extend toward 4th gear. These were making the slider not move easily. This likely contributed to poor shift quality.
Bent spring shown on the left, OK looking one on the right.