Notchy shifting and feeling bumps while shifting in to gear

Ventruck

Not sure about the BRZ (I thought that required aftermarket tuning to enable rev match), but there's no reason Nissan would deliberately make the car rev more than it should when the engine is disconnected to the drivetrain.

I'm guilty of this slip-up too, and I think it was attempting a quick 4 → 5 shift also. Engine just runs to the limiter. Of course, you wouldn't really want to hang at redline either, but the occasional hit shouldn't be a big deal.