I just stumbled across this question and thought I'd add a few valid reasons as to why the truck may not have been auto-driving. [NOTE: I haven't watched this in a while so the wording of my quotes might be slightly off.]
Technology takes time to spread
As far as I can remember, it's never stated when Spooner's accident took place, but given the amount of surgery and physiotherapy he would have had to undergo for his injuries, it was probably a few years before the story takes place. In 2035, auto-drive is certainly commonplace, but it isn't mandatory or universal - it would logically have been even less commonplace when the accident occurred.
Furthermore, it's possible that the accident itself, and others like it, accelerated the adoption of auto-driving, leading to the apparent ubiquity seen in the film. A truck driver killing a 12-year-old girl after falling asleep at the wheel, when his truck could (and maybe should) have had auto-drive equipped? People would have been outraged.
Technology is expensive
A modern electric car, even with thousands of pounds/dollars of government subsidies, is still a lot more expensive than a comparable petrol-powered car. I dread to think how expensive a self-driving truck would be in comparison to a modern manual truck. It's entirely possible that the truck company kept using outdated manual trucks in order to save money. If I had a penny for every time a real-life company's penny-pinching has ended in disaster, I'd be a rich man.
Technology is unreliable
Granted, humans make mistakes, but so do machines and computers. They break down. They malfunction. They do things we don't expect them to (like start a Zeroth-Law Rebellion, for instance). And so many people, Spooner included, trust the judgement of a human over the judgement of a machine.
SPOONER: 11% is more than enough. A human woulda known that, but a robot... there's nothing in here. [points to his chest] It's just lights and clockwork.
A modern example would be satellite navigation systems, which have been known to lead truck drivers down impossibly narrow paths, or into the middle of fields, or the ocean. So either the company owner didn't trust the auto-driving system enough to install it, or the driver didn't trust the auto-driving system enough to use it.
Technology is confusing
These new-fangled whatchamacallits can be pretty baffling to some people, especially if they haven't been taught how to use it properly. There's a story about an elderly woman who put her campervan on cruise control and then went into the back to make a cup of tea, thinking the cruise control would steer for her as well. It didn't. The campervan crashed.
So it's possible that the driver didn't know how the auto-driving worked, and figured he could take a quick nap and the computer would take over in the meantime. Except it didn't.
An interesting parallel
I want to point out something that I myself didn't realize until I started typing out this answer:
SPOONER: The truck driver... his name was Harold Lloyd. Like the film star, but no relation.
Harold Lloyd (the actor) was a star of black-and-white silent comedies, which were rendered obsolete when talkies and Technicolour arrived, thus ending Lloyd's career. It's possible that the film-makers used the name "Harold Lloyd" as a deliberate allusion to the idea of people being made obsolete by technology, a theme that's also touched upon in Spooner's first conversation with Robertson (mentioned in @sampaco's answer).
With that interpretation in mind, you can imagine that Harold took one look at a self-driving truck and either thought, "That things's going to take my job, I don't like it", or "That thing's going to drive me into a hedge; I don't trust it". Either way, I don't think he'd be setting foot in one, and that sadly led to his demise.
Regarding your points
I respectfully disagree with some of your interpretations.
Dr Calvin expresses disbelief that Spooner is manually driving the vehicle
Because he's going at about 150mph at the time. And talking on the phone. It really is safer for him to leave that to the auto-driving system. Calvin doesn't seem to have a problem with him manually riding a motorbike on two other occasions in the movie, because those times he's going at more manageable speeds.
Later in the movie, he is berated by his superior when they think he caused an accident in the tunnel
The important bit here is "they think he caused an accident in the tunnel". Borgen isn't berating him for switching to manual, he's berating him for switching to manual for the sole apparent purpose of running two USR trucks off the road. If there was an obvious reason for him to have switched to manual, I don't think Borgen would have had a problem with it.
In the movie it is generally accepted by society that the automation is bullet-proof
No. It is generally accepted by society that the Three Laws are bullet-proof; specifically, that robots cannot commit crimes, ever.
CALVIN: Face it, a robot could no more commit murder than a human could... walk on water.
But a piece of automated software consists of much, much more than just the Three Laws. There are hundreds, even thousands of things that could (and probably do) go wrong. I don't think we can extrapolate that 2035 society, as depicted in the film, blindly believes that all automated systems cannot possibly fail, ever.
- While the film doesn't seem to contain a definite explanation for why the accident happened, there are enough possible (or even likely) explanations that I wouldn't call it a plothole.
- I spent way too long writing this answer.