How can I fix "unbalanced brackets" in my data tag?

Often, when making a command block contraption, you need to set an entity's data tag. These tags can sometimes be very long, with many layers of nested curly and square brackets. For example, this is the command to summon a villager with a single custom trade:

/summon Villager ~ ~ ~ {Profession:3,Career:2,Offers:{Recipes:[{buy:{id:minecraft:diamond,Count:6b}},sell:{id:minecraft:diamond_hoe,tag:{ench:[{id:16s,lvl:10s}]}]}}

The single-line command block interface of Minecraft makes it incredibly difficult to find and fix errors, especially when it comes to mismatched brackets. In fact, for illustration purposes, I put an error in the above command.

What techniques can I use to find and fix unbalanced square or curly brackets when writing long and complicated data tags?

The easiest way to find mismatched braces is to expand the command into a multi-line format with properly indented lines. This makes it easier to find errors and subsequently fix them.

A nifty little tool to automatically format your data tags can be found at http://jsonviewer.stack.hu/. Using the Format and Remove White Space buttons, you can expand or collapse your command, respectively. Using the sample data tag given in the questions, we can turn this

{Profession:3,Career:2,Offers:{Recipes:[{buy:{id:minecraft:diamond,Count:6b}},sell:{id:minecraft:diamond_hoe,tag:{ench:[{id:16s,lvl:10s}]}]}}

into this

{
  Profession: 3,
  Career: 2,
  Offers: {
    Recipes: [
      {
        buy: {
          id: minecraft: diamond,
          Count: 6b
        }
      },
      sell: {
        id: minecraft: diamond_hoe,
        tag: {
          ench: [
            {
              id: 16s,
              lvl: 10s
            }
          ]
        }
      ]
    }
  }

Now all that is left is compare the opening and closing brackets at each indentation level. You can see that there is no closing bracket at the last indentation level, the last bracket is indented once, showing us that there is a closing bracket missing on some level.

If you check all the tags starting at the top, you can see that there's a problem with the sell tag: There's a closing square bracket instead of a curly bracket on that indentation level. To make this even more visible, we can copy-paste our data tag into an advanced text editor like Notepad++, which highlights matching brackets for us:

Have the missing curly bracket problem:

Here it is immediately apparent that a closing curly bracket is needed for the sell tag.

Without the missing bracket: