[Pwnage 2.1] Error 2001/1600 - SOLUTION
Please read the reasoning here as I have tried to be as complete as possible and would like to hear from people for whom this doesn't work, to help identify real solutions. This necessarily makes things a bit... lengthy ;)
I tried to upgrade a 1.1.2 iPhone that was activated/unlocked/jailbroken by an unknown method to 2.1 using iTunes 8 and OS X 7.5.5. Pwnage tool 2.1 seemed to be working well, but failed the first time after going into "DFU mode" and starting iTunes to do the custom restore. I tried for an hour and a half various methods and tips to get this working again before fixing it and I would just like to give a suggestion and explanation that might help some people.
I tried many different things that I found on the forums here and elsewhere that people claimed had fixed their 2001/1600 error and they didn't work. I also read that it didn't work well on OS X 7.5.5. FWIW, I think people are linking the cause and the solution incorrectly - things that are working for some and not others are likely coincidental. I tried removing the SIM, various types of restore sequence, checking iTunesHelper was shut... God knows how many things. None of these worked. Here is what happened to me, how I solved it, and what I think the problem is:
I first used normal restore 2.1 from iTunes, unpwned.
I ran Pwnage 2.1 and let it do its thing, choosing all the options (see guide at sleepers.net for Pwnage 2.0 if you don't know the process already)
Pwnage says it successfully entered DFU mode (screen is BLACK)
iTunes starts, says it recognises phone in recovery mode, SCREEN GOES WHITE, gives error 2001 and doesn't recognise the phone after that (i.e. disappears from left hand pane in iTunes)
I get the phone out of DFU and do random stuff for a couple of hours without success (note one of these things was to DFU restore the phone to uncustomized 2.1 but I *really* don't think that this is relevant - see below). Mostly I am getting 1600 errors whatever I try.
I decide to just start again from scratch. I don't even bother restoring to uncustomized 2.1 again as I figure the errors are preventing anything being modified on the phone.
I go through exactly the same process as the first time, get in "DFU mode" BLACK screen.
iTunes loads, phone in recovery, 2001 error as before with WHITE screen. All the same. At this point, I note that there is general confusion about exactly what constitutes DFU mode - some people say black and some people say white. I remember that when I had severe problems a while back with a different phone's wifi DFU mode was always colourful in some way.
SO, SIMPLY: quit itunes and start it again without touching the iPhone. i.e. screen STILL WHITE when iTunes starts, NOT only after starting recover like before.
iTunes recognises the phone in recovery, and I restore the custom ipsw successfully, followed by restoring the backup of the phone's settings etc. Everything works perfectly!
Here is what I think is happening: you have to have the white screen. there may be timing issues, and maybe iTunes can sometimes switch from black screen to white and carry on without error, alleviating this problem for some people. There tends to be a lack of information when things work properly, so we often don't know what people on the phone when Pwnage works - they just say "works for me!!!! thnx!!"
There does seem to be some disagreement on what exactly DFU mode is. I think people go off trying all kinds of things like I did, but just happen by luck to get the timing right when it succeeds, and attribute the success to some weird thing they did. I did restore at one point in what I thought was DFU mode (black screen) to official 2.1 but I strongly suspect this didn't help as the error after that was exactly the same. If you have severe problems maybe try this uncustomized "DFU" restore just in case.
You can use Pwnage 2.1 with iTunes 8 and OS X 7.5.5 to unlock, activate, jailbreak a 2G iPhone. You can do this even from old unlocked firmware of unknown origin. You can restore phone backups. Everything works.
If you are getting error 2001 when first going to restore from iTunes after Pwnage puts you in DFU mode: the phone should have nevertheless gone to a WHITE screen - just quit iTunes, don't touch the phone, restart iTunes and try again.
If you are getting error 1600 this may also help.
Even if you are having other difficulties not mentioned here, I would suggest that you aim for getting it in "white screen mode" before custom restore from iTunes as the first solution.
Of course I could be making the same mistake of identifying the wrong cause that I'm accusing you all of........ ;) I will be interested to hear when this does or doesn't help people.
My idea here is that timing of getting into DFU mode is the real issue. Whilst what I say here may well help you if you get error 2001, volkspost's advice below sounds like it would reduce the chance of even having this problem in the first place, by shrinking the opportunity for error. Please try that first.