It would be helpful for debugging/troubleshooting purposes if the Git plugin logged the version of git being used (i.e., the output of git --version) to the console before starting the cloning process. Additionally, if the version of git being used is not supported by the plugin, a warning should be logged to the console.
One practical application of this would be a situation like
JENKINS-62534. We were not aware that our Jenkins master agent was still running git 1.8.
When alerts are needed for unexpected global conditions in the git plugin, it could be done through a similar user interface technique as is used by GitHub webhooks. A number appears in the top right of the Jenkins interface. When that number is clicked, a dialog appears that includes a "View" button that would open a page that lists all the problems of that type. The "Dismiss" button would clear the contents of the page that lists all the problems of that type.