Apostophes showing up strangely

Trying to resolve similar over here:
http://wordpress.org/support/topic/background-32

Can you be more specific on where you are entering the apostrophe?

In the above post @electricfeet confirmed that apostrophe cannot be used in Custom CSS, has to be setup in child theme.

Is that any help?

The WordPress codex has a function, wp_specialchars_decode() for displaying HTML encoded characters such as the quote.

For displaying the quote and the apostrophe in the slider, in your child theme, simply wrap the output string in the wp_specialchars_decode() function.

For the slider, modify parts/class-header-slider.php in your child theme as follows:

Find the following code:

$text               = esc_textarea(get_post_meta( $id, $key = 'slide_text_key' , $single = true ));

Change it to:

$text               = wp_specialchars_decode(esc_textarea(get_post_meta( $id, $key = 'slide_text_key' , $single = true )));

Likewise, if you want quotes or apostrophes in the Featured pages text, modify parts/class-content-featured_pages.php in your child theme as follows:

Find the following code:

<p><?php echo $text;  ?></p>

Change it to:

<p><?php echo wp_specialchars_decode($text);  ?></p>

Hope that helps!

Mike