A document that has obvious spelling mistakes is opened in LibreOffice Writer. When spellcheck is performed, it reports that The spellcheck is complete and there are no spelling errors.
This problem seems to be something related to the language settings in LibreOffice. I was able to get it to perform a spellcheck correctly by explicitly changing the language in the document.
To do this, choose Tools > Language > For all text > English (USA). Writer immediately showed spelling errors with red squiggles and running spellcheck showed up these mistakes for correction.
If you want spellcheck done in some other language, then choose Tools > Language > For all test > More. In the Locale Setting dropdown, choose the language you want. It will now be added to the list shown in Tools > Languages > For all text. Choose it there for spellcheck in that language.
Tried with: LibreOffice Writer 126.96.36.199 and Ubuntu 12.04 LTS