I created a custom-index.php template by copying and modifying the index.php page.
The home page should have a few widgets under the header.php (which work fine) and the bottom of the page should have the latest posts shown in reverse chron order.

If I go to dashboard->settings->reading->front page displays:
“your latest posts”
The page shows only the latest posts – not the page with the additional widgets created in the custom-index.php template. As seen here is http://harrisonresearchlabs.com

If I change the to dashboard->settings->reading->front page displays:
“a static page, home page”
The page shows the widgets as created in custom-index.php, but the place below where the posts should be shows a empty post with a weird date as seen here. is http://harrisonresearchlabs.com/home

The current setting is: dashboard->settings->reading->front page displays:
“your latest posts”

what browser are you using? Try FireFox if you aren't and see how it looks.

its working fine now. The weirdness was I had created a post with just a title, no content, then deleted the title. Apparently a post with no content and no title is not the same as deleting the post itself. Listing all the posts displayed the phantom post and once I deleted the post, things behaved normally.