The 2005 Closer clip alone doesn't convince me that Katic had a nose job. I still think there's a chance she was using a prosthesis during her Closer appearance. Less that a year after Katic's 2005 Closer appearance she was in several episodes during Season 5 of 24 and her nose looked just like it does now. I was able to check out how Katic looked during Season 5 of 24 only because I own the DVDs.
Does anybody have access to anything Katic did before the 2005 Closer? That would solve the riddle but, unfortunately, I don't have quick access to any of those.
When I watched the Castle season opener, I thought that Katic had lost weight over the summer, which I thought worked to her benefit this season. It makes sense that Beckett would have lost weight following so profound an injury. Anyway, Katic's weight loss didn't hurt her looks, to say the least.
EDIT: I didn't see the 2005 ER clip that Don posted until after I posted the foregoing. I now agree that Katic got a nose job, which had to have been done sometime after her 2005 Closer and ER appearances but before her 2006 appearance in Season 5 of 24.