Q:

Is extracting an ISO safe? 

I downloaded the Windows 8 Enterprise Evaluation ISO, but last time I tried to update I extracted it with WinRAR to the desktop.  I got an error during the installation.  Here are the reasons I can think of:

Corrupted download because of pausing it
Extracted it to desktop and the desktop was moved to windows.old folder, so the files weren't found
WinRAR corrupted it

If it's the second one, Is it OK if I extract it to C:/, because those files don't get moved? 

A:

Corrupted Download ? 
You can rule out this theory by verifying the download using MD5 or SHA1.   Either hash algorithm will work.   But most likely, not the problem here. 
Extracted it to desktop… ? 
The location of where you extract the file should not matter in this case.   The more important detail is file type.   Your downloaded has an .iso extension, which would lead me to believe you do not have to extract anything with winRAR.   By nature, an .iso file is an archive of an optical disk.   Moreover, the single iso file is a collection of all the files on a CD or DVD.   You really have two options: virtually mount these types of files or burn them to a disk and use. 
What to actually do
My suggestion is to burn the iso file to a CD or DVD (depending on its size), and boot your computer off the newly created disk.   Because you are installing a new OS, the virtual mounting option would not be the best idea.   
When you burn the iso to disk, you may need to specify that the new disk is an iso.   Lastly, don't forget to change your BIOS boot order!  
Safe ? 
To address your original question, is it safe to extract an iso?   I'm not entirely sure you're asking the right question.   Is is safe to run an iso?,  seems a little more accurate.   
Short answer: no.   The contents of the iso could be anything.   You must ask yourself, Do you trust your source?   If this was downloaded from microsoft.com and the hash matches, you're as safe as you can possibly be.   If you downloaded some torrent, then best of luck to you

