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Last updated March 16, 2011.
This list was previouly being maintained at http://groups.drupal.org/node/10569
This is a list of issues in the D7 issue queue that pertain to search. They've been vetted and confirmed to be real issues. They cover the entire spectrum, from advanced feature requests to bugs to theming issues.
For previous Drupal versions, check the issue queue directly.
For Drupal 7, you can also check the issue queue, as all of the issues in the search.module component have actually been vetted as real issues that need fixing. This list may become out of date, so probably the issue queue is the best place to look.
For Drupal 8 and beyond, please see the attached page: http://drupal.org/node/717654
Important Drupal 7 bugs
Probably most of these should be moved to the Drupal 6 queue when fixed.