Time Machine uses special "deny everybody everything" permissions. You should
not change them.
FIrst, do a +Repair Disk+ (not permissions) on the TM volume via DIsk Utility (in your Applications/Utilities folder).
If that doesn't correct it,
If you only have a partial backup, or don't need the ones you've done, the simplest thing to do is just
erase the disk/partition.
If you don't want to erase it, here's a workaround:
First, you need to find the name of the hidden file that's causing the problem
Click here to download the +Time Machine Buddy+ widget.
It shows the messages from your logs for one TM backup run at a time, in a small window. If it shows a message like this: "You do not have appropriate access privileges to save file “.<nnnnnnn>” in folder <Name>"* skip to *Open the Terminal App* below.
If not,
Click here to download the +Tinker Tool+ app. It allows you to change the Finder to show hidden files (among many other things). Select the first option under
Finder, then click +Relaunch Finder+ at the bottom. Reverse this when done.
In a Finder window, select your Time Machine drive/partition. The very first file shown should have a name consisting of a period (dot) followed by 12 numbers and/or letters. (This is your Mac's Ethernet address). Copy or make a note of it.
Open the
Terminal app (in your Applications/Utilities folder).
In Terminal, the prompt looks like this:
user-xxxxxx:~ <your name>$
(where <your name> is your short user name). It's followed by a non-blinking block cursor (unless it's been changed via Terminal > Preferences).
At the prompt, type the following
exactly as shown, substituting the name of your TM drive
exactly, including any spaces,
between the quotes; and the string of numbers & letters from the message where the series of x's are (keep the dot):
<pre> sudo chmod 644 /volumes/"TM drive name"/.xxxxxxxxxxxx</pre>
example:
sudo chmod 644 /volumes/"TM Backups"/.0a1b2c3d4e5f
Press
Return. You'll get some warnings and a request for your Administrator's password. Type it in (it won't be displayed) and press
Return again.
Then try a +Back Up Now+ from the TM icon in your Menubar, or by control-clicking (right-clicking) the TM icon in your dock.