When creating an old fashion block in Drupal 7 you should try to use the new render() function in Drupal 7. It takes a bit getting used to, especially when it comes to passing variables to a theming function.
This is probably how your current block content would look inside a hook_block_view() function:
$block['content'] = '<p>some HTML</p>';
This will work as expected, but if you want to use the render function it should look like this:
$block['content'] = array( '#markup' => '<p>some HTML</p>', );
Pretty basic stuff. Now once you start using some of the build in theming functions in Drupal 7 it gets a bit more complicated.
In a project I am currently working on I wanted to use the theme_image_formatter function build into Drupal 7 in order to output an image coming from facebook’s graph API.
This is how the code looks inside the hook_block_view()
$block['content'] = array( '#theme' => 'image_formatter', '#item' => array( 'uri' => 'hello.png', 'alt' => 'hello', 'title' => 'some title', ), );