I didn't see this listed in the first page or so of topics, and it also didn't see it in the Checklist of Problems section of the main website, so I thought I'd mention it because it nearly drove me crazy. When you download LT for OO or LO the download name is correct-
-however the file that ends up on your computer is LanguageTool-3.1.zip. I don't know if this is a problem with Windows, or Explorer, or what, because even going to the downloads page and selecting the .oxt file won't work. You still end up with a .zip on your computer. This is uninstallable. (I spent a long time trying to install the various .jar files inside the .zip.) You must rename it LanguageTool-3.2.oxt (and do so WITHOUT unzipping it first.) Once you do this you can use Open Office's Tools/Extension Manager to add it.
If this is something that happens commonly, perhaps it should be added to the checklist.