Well, I do the search "error 1003" on google and find out that there are many ppl have the same problem when patching the game. And here are some suggestions I collcet from google:
1. You internet connection is low speed or the speed is unstable. If you have this issue, you can download the patch when the internet is not so busy (i.e., early in the morning or midnight).
2. Maybe have some problems on the file called geometry_1.pak. For this problem, try to move the files to the root folder and renaming the test folders in the download directory.
Hope this can help you.
PS: I collect other rift errors and suggestions from rift official forum
Error 1007 - New version doesn't match expected result.
http://forums.riftgame.com/showthread.php?50409-Error-1007&highlight=Error+%23
Error 1008 - Failed to move existing files
http://forums.riftgame.com/showthread.php?51897-Failed-to-move-existing-files-Error-108
Error 1031 - Patch Failed
http://forums.riftgame.com/showthread.php?66242-Error-1031&p=1042820&posted=1#post1042820
Error 1034 - Connection Timed Out
http://forums.riftgame.com/showthread.php?66019-Error-1034&highlight=Error+%23
Error 1618 - Another installation in Progress
http://forums.riftgame.com/showthread.php?52266-Error-1618&highlight=Error+%23
Error 1935 - An error occurred during the installation of assembly component
http://forums.riftgame.com/showthread.php?64732-Error-1935&highlight=Error+%23
Error 2002 - Not authorized to play this game
http://trionworlds.custhelp.com/app/answers/detail/a_id/409/related/1
Error 2005 - Failed to connect to authenticaton server
http://forums.riftgame.com/showthread.php?50908-Error-2005&highlight=Error+%23
Error 6001 - Need Administrator Rights
http://forums.riftgame.com/showthread.php?32388-Beta-install-problem-Error-6001&highlight=6001