The absence of grammar checker is a major gripe I always hear against OpenOffice. Yes OpenOffice does not have its own grammar checker, but you can easily add one.
After the Deadline is an extension for OpenOffice which can check your grammar. Well, according tho their website, they do not describe it as just a grammar checker. According to them, it is a contextual spell checker, advance style checker and intelligent grammar checker. It is developed by Automattic, which also makes WordPress.
Anyway, to use the After the Deadline extension to OpenOffice, you need to have OpenOffice 3.2 and Java 1.5. If you have both, go to their website and download the extension. Installing the extension in OpenOffice is pretty easy and the instruction is also given in their website, so I won't bother writing it here again.
To use the After the Deadline extension, you need to have an active internet connection. I tested it for a while and I can say that it works quite well.
There are also a lot of options available.