However, I’m not aware of any version of Markdown that gives a special meaning to a row of tildes. Two tildes are generally used for strikethrough font (coded as ~~strikethrough~~). Regardless of how it’s supposed to be interpreted, the <br /> should never show in the final rendering.
some implementations of “extended” markdown use three tildes ~~~ to mark the beginning and end of blocks of code. so that’s why you see a gray box around the resulting text. the extra <br /> seems to be related to whatever was going on in that other bug report, and there also seems to be the additional problem of stuff after the first <p></p> not getting formatted properly (also mentioned in that bug report discussion). once you begin the code block using ~~~, you can’t seem to close it with a subsequent ~~~.