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Yeah... if you're using the Wordpress platform hosted through Wordpress instead of through an independent hosting solution then you can't add plugins so you're a bit stuck on that as far as my knowledge goes.

In the case of the wordpress trackback issue... its basically self-referential. Because their is a link to your blog post on your blog, wordpress creates a trackback to notify you their is a link to your blog post on a blog. Normally the reason for this is to notify you of when someone else on a blog posts a link to your site or posts on one of their posts. I.E. a Pingback or a trackback. 302s may not pass link equity but the trackback won't pass as much as the link that the trackback is notifying you of in the first place. So ultimately, don't worry about the trackback 302s if you can't change the wp-trackback.php file. Its an easy fix if you can access the file but otherwise the seo benefit in this particular case is neglible. Your old blog URLs 302ing is an issue though. Have you double-checked with the SEOBook tool that your URLs are redirecting improperly or is it just the trackbacks that you're being warned about?

Thank you, William!  Very helpful and much appreciated.