Posting my solution for weekly permalinks, as the solutions I found in the forums had a lot of errors.
This is for the links:
{date_heading display="weekly"}
<a href="/news/week/{entry_date">Week of {week_date format="%d/%m/%Y"}</a>
{/date_heading}
The resulting urls look like this: example.com/news/week/2012-08-06
This is for the permalink page (I’m being lazy and making them in a different template, perhaps later on I will put them in the same template).
<?php
// get the entry date from segment_3. If empty, use Monday of the current week.
$entryDate = $this->EE->uri->segment(3, date('d.m.Y',strtotime('last monday')));
// append minutes and seconds to entry date
$startDate = date('Y-m-d', strtotime("$entryDate")) . " 00:00";
// add 7 days to entry date, append minutes and seconds
$endDate = date('Y-m-d', strtotime("+7day", strtotime($entryDate))) . " 23:59";
?>
<ul>
{exp:channel:entries channel="news" dynamic="no" disable="member_data|categories|pagination"
start_on="<?php echo $startDate; ?>" stop_before="<?php echo $endDate; ?>"}
{if no_results}There are no results for the chosen week.{/if}
<li>{title}</li>
{/exp:channel:entries}
</ul>
Allow PHP on template, parsing stage Input.
Now, if I could only navigate between weeks :(