Well, assuming our society is radical enough to discard identity, I think we can fix the prison system. The first step is to rethink what "crimes" are. Smoking marijuanna is not a crime. Selling it is not a crime. We should reserve prison for people that have proven they can't be in the "normal society" anymore. That basically means murders, rapists, "real criminals".
The next step is to make prisons centers for removal from society, not a place where we throw "undesirables" and let them rot (like the current system). We should give people in prison freedom to have a job, freedom to buy things, etc. We shouldn't force someone to live in a 16 square foot concrete box with 3 other people for 25 years. That's torture, not rehabilitation. (Other countries do a much better job than the US in this respect -- so this isn't just pie-in-the-sky. It could work.)
So anyway, I'm idealizing, not suggesting a policy. If someone is a danger to society, it doesn't benefit society to give them an identity document. Unless they are completely stupid, they are just going to fake the document to get what they want. (Example in real life: college students. It's illegal for them to buy alcohol, but they want it anyway. So they just get a fake ID. Problem solved. But why make them criminals for this? Why not just let them buy the beer legally?)
How did they know that he was correctly identifying them?
<rimshot />
In all seriousness, though: Once they'd caught their suspect and thrown them in Newgate Prison, the authorities could always summon people from the suspect's hometown to ID them more precisely. In theory. In practice, that would surely have been very expensive and slow, and I have no idea how diligent they really were about all that pesky "legal procedure" stuff, particularly if the prisoner didn't have the money to hire a lawyer. Back then they charged prisoners for everything: you had to pay room and board in prison, so if you hadn't managed to hang onto your money (which was probably pretty difficult when you were being arrested by freelance thief-takers...) and you didn't have local friends to look you up in prison and help pay your bills, you could be stuck in there for life, like Charley on the MTA.
How do yo correctly identify someone by sight?
Everyone who can talk (and I would guess grunt or otherwise shake the vocal cords) has a voice signature. The difference in some might be minute, even undetectable by most people, but the difference is still there.
People who have lost their sight tend to pick up more on the other senses (unless there's some damage there too). Consider braille. Can you distinguish the different dots?
Oh, man, we've got enough indefinite imprisonment without charges going on as it is. Please don't encourage it.
Once upon a time, people's "data shadows" were very thin indeed. In The Fatal Shore, a truly awesome history book about Australia, they talked about policing in Georgian England. The identification of criminals relied primarily on verbal descriptions of their looks:
Official crime records and registers of criminals were primitive, and there would be no fingerprinting until 1885. Artists made sketches, for popular consumption, of famous offenders... but one could no more recognize a felon from such semi-devotional effigies than pick St. Paul from a crowd by consulting a Byzantine icon. Identification of wanted men had to be made from verbal descriptions in the police gazettes, circulated to mayors and magistrates after the early 1770s... Sketchy as they were, such descriptions did produce some arrests, mainly in villages where people noticed strangers. Some officers of the law had long memories. Henry Fielding's sightless half-brother John, a magistrate known in Bow Street as the "Blind Beak," was said to be able to identify 3000 different malefactors by their voices alone. But on the whole, it was easier for criminals to escape scot-free in the 1780s than it would ever be again.
This meant that, once you had caught a suspected criminal, there was no way to release them temporarily without them disappearing, quite possibly forever. So a lot of crimes were punishable by fines (which could be collected on the spot), or by immediate imprisonment (which is what you got if you couldn't pay the fine), or by death. You couldn't really put people on probation, or parole, or release them on bail.
The result, in practice, was that every person who stole a loaf of bread risked indefinite imprisonment or even death. It was so inhumane (and so expensive -- there weren't enough jails) that the English legal system leapt at the opportunity to solve the problem in a novel way: Transport criminals to the colonies, where they would never bother homelanders again even when they were freed. Until 1776 the favorite colonial destination was the American colonies, but after that the English had to invent the Australian penal colonies...