I'm having trouble with items that are 100% in width and a float is in the same container.

For example

<div style="float: right;">testtestest</div><h1>Test</h1>
asdasdasdasdhasuasdjahsdkjasdjkhasd

The h1 would run through the float. This interferes with links and if it has a border then it is visible under the float.

Any way of fixing?

a floated element cannot be 100% wide, it HAS to have a fixed width applied to it.

Floats exist in a separate plane (or layer if it makes it easier) to block elements and you have to tell the non-floated block elements how much space to allow for this plane.

I'm not trying to 100% a floated element. Though I have found a quickfix which is apply overflow:auto; to the offender. Wish there was a more global way to fix it though.

The point here is that when you float something, it MUST have a defined width.
Then you must CLEAR your floats.

It's nothing to do with clearing it I guess. It's just that H1 has a border and it goes through the float.

Set the h1 to display: inline.