I'm deleting my wordpress installation because at the moment it's a mess. When I reinstall wordpress, it will be on a different subdomain and the posts will be at different URLs (also the site will have a different design, but I doubt that matters). How do I make sure Google doesn't get "confused"? Any way to get it to reindex my whole site?
site will likely get reindexed, be careful for duplicate content penalties as google treats a subdomain like a different site...
If your existing blog is really mess and the content yet not listed you can simply off it and import content to newer blog, if the content is listed and you've good number of backlinks you should do 301 redirect as suggested by miranon.
If you cannot 301 redirect it, then eventually Google will get 404 not found status on your old URLs and stop indexing them. Then you won't have to worry about duplicate content. But if you can 301 redirect from old to new, it will help you preserve any link authority your old URLs had and just be a much smoother transition overall.