This...could be really really bad.
EDIT: Blunty expands on GameXplain's video.
The Joy-Cons are using a very low bluetooth signal strength. and our human body(mostly made out of water) blocks the high-frequency radio waves used in bluetooth. The signal is low because Nintendo wanted the Joy-Cons to have 20 hour battery life. A software patch will not fix the issue. Nintendo needed to foresight to allow firmware updates to the Joy-Cons in order to fix this. Let's hope that's the case?
Of course the higher signal strength means a sacrifice in battery life. So...guess you'll have to spend an extra $30 on that stupid charging grip after all.
Also, as if that wasn't enough, Syrenne points out on Twitter that "increased signal strength of Bluetooth 3.0/3.1 notably interferes heavily with LTE and mobile phones, which Switch uses."
So there's the very real possibility that Nintendo has already totally screwed this up in so many ways.
I SWEAR THIS IS THE LAST EDIT: This is probably the reason why the Switch will not support BT headsets or speakers.