I notice that I can draw on the live map. Initially I thought this might be a way to create a flight route or path. However I cant find a way to then tell the P3 to fly that path.

Is the above possible.

Also, is they any way to fly the P3 in a relatively perfect wide circle and keep the camera pointed at the centre all the time. For example, fly it around a building and take a 360 video of the building?

Neither of those things are possible right now. The Phantom manual does mention that the point of interest feature is in development though.

Goto YouTube and search for "Demunseed" videos. He has one that shows  how to circle an object and keep that object in view. He uses an incredibly low-tech (a cereal box top) idea for an incredible effect. When he discusses "pinching" the box stop, I was a little confused. It quickly made sense.

Also, I assume when you say you want to circle a building, let's hope your P3 will be high enough to be visible the entire time!

The map draw feature is simply that - you can draw lines, rough circles, arrows and even notes on the screen with your fingers as reference or reminders before or during a flight.  For example - an arrow pointing to a tree with the note "Nest".  There is an eraser symbol on the screen that will erase whatever you've drawn.  

I own an Inspire 1, a Phantom 2 Vision + Rev. 3, and a Phantom 3 Pro.  Of these, only the P2V+ Rev. 3 currently has waypoint capability (up to 16 waypoints) and it works great!  I can set location and altitude at each point - press GO - and the P2V+ will automatically take-off and fly to each point I've set on the map, while I still control camera gimbal.  Even if I lose controller connection, the P2V+ will complete the waypoint flight and return to hover over the home point.  I then land the quad manually.  I use it all the time.  Inspire 1 owners have been waiting for this feature for 4 months.  I suspect that the Inspire and P3 will both get this feature at the same time in a couple months in an update to the DJI Pilot app.  DJI sources on this forum indicates DJI is working on this feature as well as a "Point of Interest" feature which will keep camera pointed at target point as the quadcopter circles around it.  Look forward to seeing both features implemented.

It's the Point-of-Interest feature that I am really after. Thx for the replies.