iPhone Jailbroken Iphone 4 stuck in reboot loop.

I wanted to remove the jailbreak on my iphone, which was at 5.0.1, and update to the latest firmware, but any attempts at restoring in itunes were not working. I kept receiving different error codes pointing to "third party interference". I tried restoring in every mode I could think of: dfu, pwned-dfu, recovery, but to no avail. At some point though, my phone got stuck in recovery, and I had to use tinyumbrella to get it out. At that point it started to boot, and the screen went black... and then it booted again, and the screen went black again. It just keeps flashing the apple logo at me, and I'm afraid to try anything else. I tried doing some research, but everyone else who has this problem seems to be fixing it via restoration, which itunes still won't let me do. At this point I just want a working device; I don't care what firmware it's at, or whether or not it's jailbroken. Can anyone help me?

EDIT: I somehow got it to reboot through redsn0w, although I have no idea why. Still, it would be nice to figure out what's going on and why I can't remove the jailbreak and update without some kind of catastrophe going down

The first one was error 21, and the next attempt gave me error 6. There was a third one that I can't recall, but after that was when I started having trouble booting it.

I'm not sure; how would I check? Sorry; I'm mildly tech savvy, but I'm still kind of an idiot about this kind of thing.

I WAS trying to update to 6.0, but I'd prefer updating to the latest firmware with an untethered jailbreak, which is believe is 5.1.1. I'm currently at 5.0.1.

A Cydia page.

Mac.

Yes, I updated recently.