There is no distance limitation, so much to the fact, that once, I was confused whether I had left my phone at home or it was at the office. Once a phone is paired with a computer, it will stay linked, even if both devices aren't using the same internet connection or gasp, in the same place. Meanwhile, messages will continue to appear on both devices. It's rather shockingly easy to default to WhatsApp Web, and realize, wait a minute, you don't even have your phone on you.
It most likely won't be long until advertisements start popping up, but until then, let's concentrate on one interesting, unintentional privacy hiccup that we found by accident: It's not hard at all for someone to read your messages.