It seems he wasn’t the first to look at the Moon through a telescope.
I wonder how history would be different if this had been widely known at the time?
Bismillah!
NO!
Maybe them Harriotian Moons of Jupiter? 
Sorry, Galileo published first. Kinda like why the Theory of Evolution really needs to be credited to Wallace as much as Darwin, although Wallace only wrote it up first.
Neither Alfred Wallace nor Charles Darwin should be credited with conceiving of the concept of evolution as it existed long previously and had wide credibility among educated people of the time. What was novel was Darwin’s theory of natural selection, to wit, that members of a species compete with themselves and of others for resources, and those which compete most effectively (as measured by their reproductive success) then propagate more prolifically with offspring that carry the same expressed features and abilities that made them most successful. It is true that Wallace conceived of a similar mechanism that drove evolutionary change concurrently and was preparing to publish, prompting Darwin to copublish with Wallace the paper “On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection”; however, there is no question that Darwin’s work in On the Origin of Species was more extensive, and his later work in support of and extending the principles of natural selection placed the theory on a very firm empirical grounding and with a strong (if necessarily incomplete, given the primitive state of microbiology of the time) theoretical basis, while Wallace floundered in different occupations and proceeded to offer little more to the emergent field of evolutionary biology. So it is entirely appropriate–if unfortunate–that Darwin is the acknowledged father of modern evolutionary biology while Wallace is a footnote.
As for the o.p., I’m unclear as to how it is known that Harriot used a telescope. The detail of the maps does not appear to be greater than could be produced by the naked eye, and the article does not establish that he used a telescope. Certainly many astronomers prior to Galileo performed many feats using the Mark I eyeball and primitive locating instruments.
Stranger
Not very different at all. England had no Inquisition to make Harriot suffer for his work–not a Catholic country, remember? Even so, evidently he was too timid to publish (“no desire to raise his profile”, the article says). Meanwhile the Inquisition would have gotten after Galileo anyway, for advocating the Copernican theory.
I don’t blame the BBC making a fuss, but I can’t see this new discovery as much more than a curiosity. Yes, Harriot was the first to use a telescope to look at the moon. What else did he do? Did Harriot advocate for the Copernican theory? Did he discover Jupiter has moons, or that the Milky Way is made of stars? Did he make any discoveries in basic physics (pendulums, falling bodies)? Galileo did do these things, and none of that is changed by this new finding.
I don’t really have anything important to add, but felt it worth stating that the Mark I eyeball is one of the finest instruments I have ever used.
Harriot’s 1609 drawing (which actually isn’t shown in the BBC story) is crude and little better than some might manage with the naked eye, but it has long been universally accepted that he used a telescope to do it. I can’t recall how explicit his 1609 notes and letters are, but there are discussions of telescopic observations of the Moon in his circles by February 1610. Since Galileo still hadn’t (quite) finalised the text of Sidereus Nuncius by March 2nd, that means that he knew about the new instrument independently. And, while the exact circumstances are murky, rumours about and examples of some new optical device were doing the rounds in 1609. At the very least, it becomes a stretch to suggest that the timing is just coincidental.
His later drawings are better and may be influenced by Galileo’s. People argue the toss over such details as by when he may have seen a copy of Sidereus Nuncius (or even whether he ever did).
Harriot wasn’t even the first to point a telescope at the heavens. It was already reported in 1608 that one could show stars invisible to the unaided eye.
Harriot was never an obscure figure in the first place - publishing The New Found Land of Virginia saw to that - but he’s probably the single person in all of 17th century science whose achievements have been most positively re-assessed in the last few decades. The late D.T. Whiteside’s judgement that he was the most important English mathematician prior to Newton had a lot to do with that. Harriot was a Copernican and it’s been realised that his work in mechanics was both comparable to Galileo’s and done earlier. If anything, his lunar drawings have simultaneously been both his best known scientific work and the least significant.
Some of his scientific contributions were known to his contemporaries and so he did have some impact, but publishing nothing limited it.
Of course, the only reason for the current publicity is that it was merely a neat way of kickstarting the International Year of Astronomy at the beginning of 2009.