The first thing to remember here is that licenses, open source or otherwise, are effective only because of copyright. Without copyright protecting your code, anyone could just take it and do whatever they like with it. Copyright law (fairly universally across jurisdictions as it's part of the Berne Convention) sets the default position is "all rights reserved", so nobody can do anything with your code except the very limited number of things allowed by fair use/fair dealing exceptions.
As the copyright holder, you are free to release your code under any license you wish. By choosing the GNU GPL, you are allowing people to do more with your code than is allowed by the default "all rights reserved" so long as they comply with the conditions of the license - but the thing to always remember here is that you are the copyright holder and can do whatever you like with the code so there cannot be a "conflict" between the GPL and your copyright: you personally are always free to completely ignore the GPL for any code you own the copyright on.
That said, if you do intend to release a piece of software under the GPL, having a line in it saying "all rights reserved" is at best going to be very confusing for anyone wanting to re-use the code. By granting people extra rights under the GPL, you have specifically unreserved some rights. I personally wouldn't touch a piece of code which was claimed to be released under the GPL but also contained that line because of the legal uncertainty.
Thankfully, the GPL gives us clear guidance on how best to indicate a program is released under the GPL - see the "How to Apply These Terms to Your New Programs" at the end of the license, although note these are not part of the terms and conditions so do not have to be followed to the letter. You should replace the "all rights reserved" line in any source file with the example text listed there.