I have a nice pair of Bluetooth headphones with mic, and as nice as they sound, the lag they introduce is unacceptable. Especially when it's been a few mins and it has to wake the bluetooth connection, it can take a quarter to a half second before I hear something that would have already been played if it were on the built-in speaker or on wired headphones.
When watching video, it makes a big difference, it feels like something is wrong with the file. When using it for voice communication, it makes a small but annoying difference.
It's not just my headphones either, I've tried others. BT headphones (and most likely speakers) suck for anything time-sensitive.