A couple of days ago, I was having some difficulties with the partitions on the harddrive that I have Helena on. Based upon the fact that I have a recent backup of my then-/home, I elected to just reinstall.

But after reinstalling, when I use the backup tool to restore /home, I get the following error message: "An error occurred while opening the backup: tar xvf backup.tar --> 512."

What to do? Any help would be much appreciated.

What do you mean "backup tool" ?
Can you open the backup manually ? can you extract it manually ?

If so, do that instead.

I just looked it up and Helena is a version of Linux Mint which comes with a "Backup Tool" utility.

@Randymanme: is that the exact error message? As smoker suggested it's worth trying at the command prompt. That is a more fundamental way of doing things and may show more informative error messages. Not knowing the content of the tar file (relative or absolute paths?) it may be prudent to use tar's --list option to see what's there first, especially if you have to be root to read the tar file. What are you hoping to restore from the tar file, possibly over your newly-installed system?