Optimizing home page

Yeap. Because sometime you unconscious that optimize some keywords that you not want in your home page. Because we are not the one to grade it but search engine are the one to grade it how relevant and quality it is .
I believe you need to restructure your content if those keywords is not what you wish to target.

Hi there, Seolvl1.

I am new to the forums, though, I will try to help in some way.

Yes you can rank for Keywords you have not optimized your pages for.

This is nothing unusual.

I would guess that your doing Bookmarking for the inner pages is achieving the required results.
On the other hand, you may be optimizing your home page, though, depending on what that optimizing is, it may have no effect, whatsoever.

If you are building back-links to your inner pages, this is supposedly a good thing. Back links to actual pages helps those pages to rank, and is one of the things people check when comparing the strength of competition. Having all your links (back links) pointing to your homepage(domain) would according to many, not help too much for ranking your actual posts.
There are many debates over this.

Google ranks pages not sites, as such.

As far as ranking for non targeted keywords, some of the keyword seo tools(even some of the free versions) will indicate certain(non targeted terms) are ranking well for you.
Though, it is common that many of those terms are low quality(low traffic volume).

Remember that if you target a keyword term, you could also possibly rank for related(or similar) terms.

Another place to check is in your Google webmaster tools and Google Analytics. What you will see is keyword search terms used by people who found your site(some are unusual) and also, terms you may be ranking for that you may not have known.

SEO is not as simple as it sounds.

Don't go for the difficult keywords, like....home based business. Too much competition.

Don't waste your time on the ultra-longtailed, non-targeted keywords like I did...earn more. You get page one with only a couple visitors.

You will find yourself optimizing for a combo you never thought of using, after you do a study of terms ranking well. There are several free SEO programs available--just google SEO.