Go into time machine and pick the folder you want to restore. Then left click, get info, in the info dialog box make sure the permissions are set to read and write. It sounds like they're set to read only for some files.
I have just tried recovering a document from a back-up disk using Time Machine, but couldn't do it because TM says I don't have permission to access "the file". (I do - I am the only user of the machine.) So I tried some tests:
I tried another document (from the documents folder) and got the same result.
I tried retrieving a movie (from the movies folder) and got it, but had to give the admin password.
I tried getting a photo (from the photos folder) and it worked perfectly.
Can anyone tell me what's going on here, and how to fix it?
(MBP running 10.6.3)