Updated to Mountain Lion, now finder requires password to create a new folder or trash one. Moving a folder to another folder copies it. Can't back up most of my files onto my backup hard drive. Tried repairing disk permissions.

Hi DAPratt,
I understand that you are prompted for your username and password for everything you do. It might be due to a permissions issue. Let's see if we can sort that out.
Start with the troubleshooting outlined below. It came from the article that describes your issue of asking for the password for each move or modifying of the files. It will walk you through updating and changing the permissions that are set.
OS X: If you see issues after using "Apply to enclosed items" on your Home folder
https://support.apple.com/en-us/HT203538

To correct these issues, follow these steps:

1. Use Software Update to install all updates until it reports "Your Software is Up To Date".
2. Open the Get Info window for the account's Home folder:
   • In Finder, select Go > Home
   • In Finder, select File > Get Info
3. If needed, click the disclosure triangle to expand the "Sharing & Permissions:" section of the Get Info window.
4. If needed, click the padlock icon in the lower right corner of the Get Info window, then enter an admin user name and password and click OK.
5. From the Action menu () at the bottom of the Get Info window, choose "Apply to enclosed items…"
6. Click OK in the confirmation sheet.
7. Wait for the process to complete.

Take it easy

User File Ownership - Reset see post by Linc Davis

You may need to rebuild permissions on your user account. To do this,boot to your Recovery partition (holding down the Command and R keys while booting) and open Terminal from the Utilities menu. In Terminal, type: ‘resetpassword’ (without the ’s), hit return, and select the admin user. You are not going to reset your password. Click on the icon for your Macs hard drive at the top. From the drop down below it select the user account which is having issues. At the bottom of the window, you'll see an area labeled Restore Home Directory Permissions and ACLs. Click the reset button there. The process takes a few minutes. When complete, restart.

Repair User Permissions