A number of people who have upgraded iTunes to the recently released version 10.1.1 have found the program will not properly launch. When they try the program will either unexpectedly quit, or display an error stating the program "cannot open because of a problem."
This issue likely has happened because of an error with the updater being provided through Software Update. People who are noticing this problem have updated through Software Update, whereas those who have used the standalone updater have not experienced this issue.
To fix the problem, the easiest approach (as discovered by MacFixIt reader "Testudo") is to remove the iTunes program from your /Macintosh HD/Applications/ folder and then reinstall iTunes by downloading the full installer from the iTunes Web page. If needed, you can then download and apply the manual update and the program should launch just fine.