I'm, looking for a plugin (or some kind of extension) for the Eclipse IDE so it can check grammar, and flag mistakes like "The dog dog is lost" etc.
I have used a tool called LanguageTool for grammar check in the past. It's an excellent free proofreading software for grammar, style, and spell checking. It also has a list of addons supporting Eclipse. The original author and the addon listed on the LanguageTool wiki is deprecated, but linked below is a fork that is said to be the successor.
Note: I have not used this plugin, however, I have used LanguageTool
Eclipse plug-in for Languagetools
This plugin contains an Eclipse plug-in to use the spell checking engine LanguageTool in the Eclipse IDE. This repository started of as a fork of https://github.com/auguster/languagetool-eclipse-plugin but as the original remote included the languagetools JARs it was recreated from scratch.
This is a screenshot from the website, which should implement the same check in the addon