A bit of history here: I'm biased. My first degree was at Manchester, and I graduated almost exactly 10 years ago. Tom Kilburn (head of the team, and the expert who was brought in because of his work on CRT based memory down in Malvern (another site I've worked at)) came to the graduation ceremony, and a different team had just finished building the replica of The Baby which is now in Manchester's science museum. And our CS101 course (taken in parallel with the other courses we were working on, and filling in the gaps) introduced us to assembly code with programming what was effectively the instruction set of MU1, of which this computer was a proof of concept. So I feel a little proprietorial.

But let's look at what's wrong with this article. And for reference, here's a brief overview which I think contains all the needed facts.

I think I'll go through this in order. Let's skip the banalities, because, well, I waffle enough as it is.

...on the morning of June 21 1948 Baby finally delivered:...

quite correct, but what did it deliver?

offering the answer to a maths problem that it had been posed a mere 52 minutes earlier.

So, wait a second, you're saying that these people are so daft that they test a machine with a 52 minute long program? Maybe they tried that after a few days, and only tried little numbers to start with.

...to solve a complex mathematical problem:

Oh, let's see what this complex problem is, then.

determining the highest proper factor of 2 to the power of 18.

right... Shall we all have a think about what the answer to this is? I guess we'll have to know what a factor is first, and then what a power is. And then maybe we'll have our answer. Go on then, is it... is it... 2¹⁷?

And yet the machine could not add or multiply — only subtract

Go on, you could write an informative and interesting paragraph about why that is. Or you could make it seem like a bizarre quirk.

Instead of storing information on a hard drive, as we do todat, Baby kept its data in a cathode ray tube — the same sort of technology used in TV screens.

Well, I bet it wasn't storing data in an LCD or a plasma cell. I'll let you get away with it though, because there's a CRT in the room I'm sitting in now.

later that year Alan Turing — the mathematician made famous for decoding Nazi ciphers

Well, I don't think he was to become famous until quite a while after he died. Of suicide. Caused by government harassment. Of course, what's written doesn't necessarily imply he was famous for decoding the ciphers at the time (a necessary but not sufficient cause for the Allied victory in WW2), but it does rather imply it, doesn't it.

an iPod can hold more than 640 million times more information

Well, it can hold 1.25 billion times more information. Or let's use the figures in your callout box: oh, a trillion times as much. Wow!

Yep:

It could store 128 bits of information, negligible today.

Certainly is negligible today. It was also pretty much useless then, giving only 4 words of memory. With 32 words, they could fit in, you know, a 17 instruction program, and still have room left over for 15 words of working memory.

The machine could perform 3.5m operations a second

Seriously? Do you know how large a million is? It's a big number. Mind-bogglingly big. Like, huge. Enormous. If you wanted to count to a million, it would take you, like, weeks. Let's have a look again. Oh yeah:

here around 130,000 numbers were tested, which took about 2.1 million instructions and involved 3½ million store accesses

So that's where 3.5 million came from. But that says 2.1 million instructions, anyway. And it doesn't say per second, does it? What does it say?

The correct answer was obtained in a 52 minute run

So that's per, err, 3200 seconds, then. Well, we're still looking at an impressive 7000 instructions per second, then. Well, it's impressive if you know what the numbers mean.

Honestly, you'd almost believe that these people were trying to keep you in awe of things, not trying to tell you all about them. That's if you give them the benefit of the doubt to assume that they understand what they're saying.

Once again, I remember why I don't like reading the paper.