What is the impact of addition of character encoding to various versions of browsers?

I have a website which has   in my code for non-breaking space, &#8226 for bullet symbol.

For my website to be read properly by another software, I need to add contenttype charset as UTF-8 to be page. Without utf-8 the software reads my page   and displays as circumflex A, bullet symbol as •

Webpage without any charset tag already works fine in IE 7, 8, 9 10.  On adding utf-8 charset contenttype header to my page will there be an impact to page view in browsers? Will there be a problem in parsing of other characters in page?