Better integrated spell checker needed
This is more of a complaint than a question.
The integrated spell checker in Firefox really, really sucks. It things that "Robert's" is different than "Robert" AND you cannot add "Robert's" to the dictionary. It thinks "ROBERT" is different than "Robert."
GOOD spell checkers are case-insensitive when checking a word ("Robert" = "ROBERT" = "RObert" etc), they know what plurals and possessives are ("Robert's" is not a spelling error). I could go on.
The original "ABCspellcheck" (?) addon was a much, much better spell checker.
Wšykne wótegrona (5)
I think what you are looking for is a grammar checker.
Go to the Mozilla Add-ons Web Page {web link} (There’s a lot of good stuff here) and search for what you want.
Words that come in an installed spelling checker dictionary behave different from words that you add yourself to the persdict.dat file. A dictionary has metadata defined via the .aff file that allows some modifications like support for plurals.
Normally only the first letter can be a capitol or the entire word, but more than one capital letter at the start is usually flagged as you may have pressed Shift for too long.
Note, using Firefox's built-in Spell Checker does not work properly because it's a hash spell checker. That's why it is case sensitive, does not recognize possessives, nor plurals, of existing words.
Firefox uses Hunspell: https://en.wikipedia.org/wiki/Hunspell
Given current priorities I don't think Mozilla is likely to adopt a new spelling component in the near future, but maybe we'll get surprised. More likely, everyone should be trying to improve Hunspell since it used in many open source projects.
See also hunspell4.pdf.
One of the major problems is that affixes aren't supported in the personal dictionary where you add your own words (an AFF file is only attached to an installed dictionary), so no modifications are supported and you would have to add all spelling variants to persdict.dat (plurals and leading capitals if the word can be the first on a line).