I think a number of other answers missed the obvious issue...
You are using mysql_real_escape_string on the inputted content (as you should if not using prepared statements).
Your issue is with the output.
The current issue is that you are calling html_entity_decode. Just stripslashes is all you need to restore the original text. html_entity_decode is what is messing up your quotes, etc, as it is changing them. You actually want to output the html, not just plain text (which is when you would use html_entities, etc). You are decoding something you want encoded.
If you only want the text version to show up, you can use the entities. If you are worried about bad tags, use striptags and allow only the tags you want (such as b, i, etc).
Finally, remember to encode and decode in the proper order. if you ran mysql_real_escape_String(htmlentities($str)), then you need to run html_entity_decode(stripslashes($str)). The order of operations matters.
UPDATE: I did not realize that html_entity_decode also strips out slashes. It was not clearly documented on that page, and I just never caught it. I will still automatically run it though, as most html that I present I want left as entities, and even when I don't, I prefer to make that decision outside of my db class, on a case by case basis. That way, I know the slashes are gone.
It appears the original poster is running htmlentities (or his input program, like tinymce is doing it for him), and he wants to turn it back to content. So, html_entity_decode($Str) should be all that is required.