In the interview (the relevant section begins at 6:22), Musk said that Tesla could increase the range of the Model S to 1,000 kilometers (621 miles) "within a year or two."
Musk noted that the Model S distance record already stands at over 700 km, although that isn't really achievable under everyday conditions.
Elon Musk interview with Danish newspaper Borsen on Sep 23 says autopilot will be out in a month, and fully autonomous driving in 3 years. It will take a few more years for regulators to allow them.
As far as reliable range in the 600-mile neighborhood, Musk said that it will definitely be possible in 2017, and perhaps earlier.
By 2020, he expects a range of 1,200 km (745 mi) to be achievable.
That's the point when Musk wants Tesla to be selling 500,000 electric cars per year.
At 5% improvement per year just in the batteries, Tesla will get from today's 300 miles of range to 382 miles in 2020, and at 10% per year, Tesla get to 483 miles in 2020.