How to pass an argument from the URL to a views exposed filter?
Assuming you are using arguments (contextual filters D7.x) you can make another display that is attached to the main display.  This attached displays should be programmed to provide a summary list when the argument is not present, and to present the list as a jump menu.  You can then set up the jump menu to select the current URL argument (contextual filter). This provides a select menu for an argument, that shows the current argument if it is specified in the URL.  An example of this is the results summary page I created for our club's main fundraising race.  

The main view page display has three url arguments: year, race category, and gender. The attached view has year as its first argument and race category as the second argument.  The second argument is programmed to list available categories (for that year since year is a required argument) if no category URL argument has been specified.  When setting up the jump menu settings it was set to "select the current argument".  The attached display is also set not to inherit the parent display's arguments.  That way when we link (main event page) to a specific category results, the selector shows the results filtering taking place and allows people to easily select a different summary.

Note -  this was done in D6.x using Views 2.16

Clarification - it is critical that the attached jump menu display is set not to inherit the parent display's arguments, but that the jump menu is set to display that argument. Otherwise the attached view won't display the jump list when the url argument is present, rather it will display the resulting content (however you set that up).  For my results summary page I had to pass the year argument to the attached jump selector view via PHP - eke!!