Many things make this a genuine candidate for "The Most Wrong Thing on the Internet Ever", but most of them can be summed up by saying that whoever made this graph has no sense of how historical evidence works; and nobody who has any sense of how historical evidence works could take this seriously. How would you even begin to use historical evidence to establish a measure of "Scientific Advancement" and plot it accurately over millenia? What causal course of events could have led to "Scientific Advancement" reaching the same level in 1000 in the alternate timeline that it actually did in 2000? And so on and so forth. You don't even need any particular specialized knowledge to see that it's looney; you could see it even if we labeled it instead as the scientific advancement of an otherwise unknown tribe over two hundred years. There is no proportion between the kinds of conclusions being presented and the kinds of evidence and inferences a real historian doing real historical work could possibly be using. One looks at it and wonders, "Why would one even think this makes sense?" And yet, it seems, some people don't look at it and wonder that.
I've noted before that historical study is in great measure a kind of causal reasoning -- indeed, it's an extremely important kind that has hardly been studied properly. And I think along these lines that some of this historical sense is just a matter of recognizing, for historical causes, the most obvious things about how causes work, that effects require causes, and that effects and causes in particular cases have to be adequate to each other.
Some of it is, beyond this, concerned with the kind of evidence historians typically work with (textual and material culture). If we're working with texts, for instance, all texts are from a perspective and for a purpose; ignoring this can mislead you very quickly. Sometimes the problem arises with handling perspectives themselves. In general people don't regard their own perspectives as unreasonable, which is why historians, faced with an apparently unreasonable perspective, are always trying to find out how it could have been seen as reasonable at the time and place and in the circumstances in which it is found. (One of the common signs of someone not having this knack for thinking historically is that they take the historian's insistence on trying to show how a perspective could be reasonable in a certain light as a complete defense.) If you're dealing with a situation in which there are a number of agents, they will have different perspectives, and it is how things seem from their perspective that will govern their actions. We can often only gather basic facts about these perspectives; but ignoring them is a good way to get things wrong. This is why professional historians are almost always suspicious of historical claims in which one 'side' is shown as very stupid or very evil. It's not that there are no stupid or evil people; it's that real life is not some crazy melodrama in which even villains go around doing things in order to do stupid or evil things. People generally have reasons; the reasons are not always good or intelligent, but you can often trace out why they thought those reasons were good or intelligent reasons. Where this doesn't seem to be in view, historians will start asking questions.
All of this is prior even to matters of detail -- familiarity with the period, acquaintance with primary sources, and the like. Thinking historically in this sense obviously doesn't guarantee correctness -- even rigorous historical analysis doesn't guarantee correctness, and we're talking about something much broader and looser here. It doesn't save from mistakes. But it does protect somewhat against the kinds of mistakes that drive professional historians up the wall -- the mistakes that should not even be mistakes, the errors that border on perverse (and sometimes pass over). As I said, there's not really any full account of what this historical good sense involves, since historical reasoning itself is somewhat understudied (particularly given its complexity); I certainly don't have one, and it might not even be possible to give a full account of it. But it's the sort of thing that's worth thinking about, if only because we really do find people waving around things like "The Most Wrong Thing on the Internet Ever".
