[html] removing bold styling from part of a header

You could wrap the not-bold text into a span and give the span the following properties:

.notbold{
    font-weight:normal
}?

and

<h1>**This text should be bold**, <span class='notbold'>but this text should not</span></h1>

See: http://jsfiddle.net/MRcpa/1/

Use <span> when you want to change the style of elements without placing them in a new block-level element in the document.