What software can check for grammar mistakes?
There is NO software that can check Chinese grammar mistakes with satisfactory results.

Automatic grammar analysis is hard. We cannot even get satisfactory result in word segmentation. (Well, this is the story in research field)

Microsoft Word has the functionality of spelling and grammar check for Chinese (it may not be installed by default in non-Chinese versions). In my opinion, the result can be far from satisfactory though.

I don't know if there is any software developed for Language Study that has this functionality.