• Auto-flag squares that must be a mine because they are one of the exact number needed to satisfy a number
• Auto-uncover squares that cannot be a mine because they are next to a completed number
  • eg an uncovered square next to a "1" that already has one flagged square must be a mine
• Reveal "possible" mines that are next to an unsatisfied number
• Shortcut to auto-flag around a number if the uncovered squares satisfy the number's requirement
• Shortcut to auto-uncover squares around a number if the number has exactly the number of mines it needs
• Auto win when no guaranteed safe squares are left

You'll always get the same game.

• Generate a random number in JavaScript and pass it as a flag for the initial seed
• Increment seed for new games

Some minesweeper games have a 'question mark' flag for when you don't know if it's a bomb.

I think this could be taken a step further by allowing the player to select tiles to group them as "one of these must be a mine".