If you right and left click at the exact same time on the world icon in the single player Select World menu then the world appears to load twice. It then puts you in a semi-spectator like mode where you can't interact with anything and you noclip through blocks.
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Game Output
21:36:15] [Server thread/INFO]: Starting integrated minecraft server version 15w44b
[21:36:15] [Server thread/INFO]: Generating keypair
[21:36:15] [Server thread/INFO]: Preparing start region for level 0
[21:36:16] [Server thread/INFO]: Changing view distance to 16, from 10
[21:36:16] [Server thread/INFO]: Kumasasa[local:E:b3e4a99b] logged in with entity id 2189298 at (821.2933612940722, 56.0, -1918.2200082205698)
[21:36:16] [Server thread/INFO]: Kumasasa hat das Spiel betreten
[21:36:17] [Server thread/INFO]: Starting integrated minecraft server version 15w44b
[21:36:17] [Server thread/INFO]: Generating keypair
[21:36:17] [Server thread/INFO]: Preparing start region for level 0
[21:36:18] [Server thread/INFO]: Stopping server
[21:36:18] [Server thread/INFO]: Saving players
[21:36:18] [Server thread/INFO]: Kumasasa lost connection: TextComponent{text='Server closed', siblings=[], style=Style{hasParent=false, color=null, bold=null, italic=null, underlined=null, obfuscated=null, clickEvent=null, hoverEvent=null, insertion=null}}
[21:36:18] [Server thread/INFO]: Kumasasa hat das Spiel verlassen
[21:36:18] [Server thread/INFO]: Stopping singleplayer server as player logged out
[21:36:18] [Server thread/INFO]: Saving worlds
[21:36:18] [Server thread/INFO]: Saving chunks for level 'Flatworld10'/Overworld
[21:36:18] [Server thread/WARN]: The save is being accessed from another location, aborting
[21:36:18] [Server thread/INFO]: Saving chunks for level 'Flatworld10'/Nether
[21:36:18] [Server thread/INFO]: Saving chunks for level 'Flatworld10'/The End
[21:36:18] [Server thread/INFO]: Changing view distance to 16, from 10
[21:36:18] [Server thread/INFO]: Kumasasa[local:E:16ddc1a3] logged in with entity id 2189311 at (821.2933612940722, 56.0, -1918.2200082205698)
[21:36:18] [Server thread/INFO]: Kumasasa hat das Spiel betreten

Is this still an issue in the most recent versions (currently that is 1.10.2, or 16w42a) of Minecraft? If so, please update the affected versions and help us keeping this ticket updated from time to time.
Can confirm, it makes you clip through the world. Using ender pearls will teleport you the the point where you would have spawned if everything was working normal.
Edit: after a few minutes the world became normal. It seems like it is a event that only occurs a few minutes.