Additional checks for spell checking.
A standard spell checker checks each word, if it conforms the grammatic rules of a language and if it is part its words. That is the core functionality. It also checks, that words, that are only acceptable as upper case ones, will not be written as lower case words (names, cities and the like).
MS Word also does a check, whether two identical words follow each other. This check can find some unwanted repetitions, but in languages other than English this can be a desired text, and not necessarily an error. For example in German "ob sie sie sah" or in Hungarian "hogy hogy csináljam meg" are correct parts of a sentence. This check is useful, but must be switchable on the fly.
An other check, checking, whether after a dot an upper case word follows, can also be useful, but a lower case word after a dot is not necessarily an error. (e.g. he was the 15. person). Therefore this check is also useful in some situations, but must be also switchable on the fly.
Other services, like checking for more than one subsequential dot, comma, semicolon, blank, etc..., and eliminating the doubles can be useful; these controls can be easily done in any text editor, therefore there is no much need for special intelligence in a spell checking applications for corrections like this.
These kind of checks should happen outside of the classic spelling library, because they must be switchable on the fly and because they are something more general and therefore should be part of the application but not of the spelling library.