4J's been busy fixing issues and squishing bugs throughout the month, and not just in the PS4 version but in the upcoming Xbox One and Vita releases too. We've reached out to the studio to confirm a delay, and whether that'll affect just the PS4 version or other platforms too. All three ports are currently due for release this month.
Sony found some issues we have to fix in their final test of #MinecraftPS4 :( We're fixing, but we need to go through the process again.- 4J Studios (@4JStudios) August 20, 2014
As for the Vita version, it's cross-buy with PS3 meaning users who bought Minecraft on the console get the handheld port for free, while new buyers will unlock the game on both PS3 and Vita. Like the other ports, the asking price to grind your pickaxe on Vita is $20.