Yes, I am seeing the same problem.
Happens only with Mavericks (Mac OS X 10.9.1). I found this in two of my VMs based on Mavericks. Thinking they were indeed bad, I just created a fresh 10.9.1 VM. Same problems reported, about "Volume Header needs minor repair" (see below for details). So all three VMs containing Mavericks report the disk problems.
I am not seeing this problem with my VM containing Mountain Lion. The Disk Utility.app > Verify reports that everything is fine.
My host machine reports no problems in Disk Utility > Verify.
I am using Parallels Desktop For Mac, Build 9.0.24172, Revision 951362.
Using a Mac mini Late 2012, with a newly replaced hard disk, and clean install of Mavericks 10.9.1 this week.
So this seems to be a Parallels problem. I don't know if this is a phantom issue or if it may mean trouble using a Mavericks VM with Parallels.
log from Disk Utility.app
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2014-01-18 16:19:50 -0800: Disk Utility started.
2014-01-18 16:19:56 -0800: Verifying volume Macintosh HD
2014-01-18 16:19:56 -0800: Starting verification tool:
2014-01-18 16:19:56 -0800: Checking file system
2014-01-18 16:19:56 -0800: Performing live verification.
2014-01-18 16:19:56 -0800: Checking Journaled HFS Plus volume.
2014-01-18 16:19:56 -0800: Checking catalog file.
2014-01-18 16:19:58 -0800: Checking catalog hierarchy.
2014-01-18 16:20:09 -0800: Checking volume information.
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Checking volume information.
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Checking volume information.
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: Volume header needs minor repair
2014-01-18 16:20:09 -0800: The volume Macintosh HD was found corrupt and needs to be repaired.
2014-01-18 16:20:09 -0800: Error: This disk needs to be repaired using the Recovery HD. Restart your computer, holding down the Command key and the R key until you see the Apple logo. When the OS X Utilities window appears, choose Disk Utility.
2014-01-18 16:20:09 -0800:
2014-01-18 16:20:09 -0800: Disk Utility stopped verifying Macintosh HD: This disk needs to be repaired using the Recovery HD. Restart your computer, holding down the Command key and the R key until you see the Apple logo. When the OS X Utilities window appears, choose Disk Utility.
2014-01-18 16:20:09 -0800:
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Last edited: Jan 18, 2014