Hi Stephen!
This is a great question, a hard one to answer, so if you don't mind, I'll answer it in reverse. I definitely think that there are things that VR and AR designers can learn from web developers, partially because I think that all disciplines have things to learn from one another, but also because these two disciplines are so close that I think there's going to be a ton of crossover. If you haven't already been following the work of Josh Carpenter and his team, first at Aframe at Mozilla and now at Google, you should do so, because he's doing a lot of really great things breaking the barriers here. Aframe in specific is a wonderful tool for developers to have a low barrier to entry to for web developers to experiment in this space.
Because there are a lot of crossover, I think some of the mistakes we will inevitably make is trying to shoehorn a 2D experience into a 3D one, or simply bevel out the way that we think in 2D. It's not great, because 3D has so much to offer, but we have to give people this time, because we stand on our shoulders and it's difficult for us to imagine outside of what's come before.
Another big challenge will be inventing rules that protect people's privacy. If we already feel like we're being violated when someone hacks our information, or harasses us in two dimensions, what does that look like in three dimensions? I think there was a study done on this that actually caused someone real emotional harm. That's a thing. We're going to have to be aware of it as we move forward.
Yet another challenge is making it so that these experiences aren't limited to the priveleged. Whether that means progressive enhancement from 2D to 3D or building better devices so that using google cardboard didn't mean feeling sick because of low framerates, that will be something we'll have to pay attention to. Otherwise companies won't build 3D experiences because it won't reach a wide enough audience.
All that said, it's an incredibly exciting time for us. There's literally a whole world we just got access to. We haven't even hit the tip of the iceberg with it. We have uneven territory ahead, but I for one, welcome our new weirdly masked faced overloads.