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

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:

To add a bit of info: I don't think that any formatting is needed, unless you have a 1000+ character command.
For begining Minecraft "programmers" I would recommend copying the command to Notepar/Gedit, finding the most indent brackets and deleting their content, then deleting the contents of the brackets "under" those and repeat untill they find a missing/wrongly placed pair.
For more advanced users I'd recommend doing it as I do: just thinking out the bracket pairs. By this way, I (and anyone else can) found the mistake in the example command in like 10 seconds without seeing the existinbg answer.

Hope was helpfull!