A glitch with the online registration system run by the O2 network meant that many people could not activate their devices at Apple stores.
The same glitch hit O2 stores but was quickly resolved, according to the firm, which is the only network to offer the iPhone in the UK.
In addition, many stores sold out within hours of opening.
The new version, which is cheaper and faster, went on sale in 22 countries.
More than 1,500 people lined up outside one Tokyo store, whilst guards in kevlar vests and helmets stood watch over 500 devices in Hong Kong.
A student in New Zealand who queued for more than 60 hours was thought to be the first to buy a device.
Jonny Gladwell waited in freezing temperatures to get his hands on the phone, which also now sports GPS.
Software glitch
"I'm going to put this on charge, have a play around with it and have a nice long sleep," he said.
In the UK many people waited through the night to be the first through the doors of stores selling the phone.
About 150 people were outside Apple's flagship store in London's Regent Street waiting for it to open at 08:02 GMT.
Student David Suen bought his place at the front of the Regent Street queue off eBay for less than £50.
He said: "I've been waiting for this since the last iPhone because of 3G."
Many shops rapidly sold out, despite some shops limiting sales to one per customer and two for business customers.
"We had queues at most stores," said an O2 spokesperson. "Where those queues exceeded the number of devices we had in the stock room, we let people at the back of the line know this first thing so they wouldn't have to wait in vain."
Both O2 and the Carphone Warehouse had to suspend online orders for the iPhone earlier this week, after "incredible demand".
Exclusive deal
In addition a system needed to register customers for an O2 contract went down on Friday morning.
"We always have resiliency built in so we quickly moved to our plan B which worked smoothly and after some initial hold ups first thing this morning we were able to process customers at normal speeds in O2 and Carphone stores," said the spokesperson.
However, Apple stores did not have access to the same back-up systems and have had to either turn customers away or collect their details to register their phones at a later date.
In the UK the iPhone is only available on the O2 network on a monthly contract. Existing customers can upgrade for free if they agree to a new 18 month contract. Other fees may apply depending on which tariff customers sign up for.
Like the first iteration, the new model is a music player, web browser and phone though the new version can use faster mobile networks and tap into location-based services via GPS. It is available with either 8 or 16GB of memory onboard.
The phone can also support programs not written by Apple. Prior to the launch Apple opened up its App Store on which can be found add-on applications for the phone.
Early applications include games, social networking applications, instant messaging and online auction software. Many of the programs are free to use and download but others must be bought.
Apple has also faced criticism from some software developers who say the process of picking which programs feature on the App Store is angled in favour of US firms.
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