Tolkien made a comment about that in one of his letters, admitting that the map was designed mostly for story purposes and regretting that he didn't research more realistic geology and such.

On the other hand, with how much trouble Tolkien had in general with finishing projects, if we waited for him to learn geology too, who knows if we would have gotten any books at all...

I just have to assume there are sinister magicks that make mountain ranges at, uh, right angles. http://www.tor.com/2017/08/01/tolkiens-map-and-the-messed-up...

One could draw a few lines at right angles on this map as well http://bogost.com/middle-earth.jpg

Amusingly that map places Weathertop fairly close to the Tap O'Noth which is ancient hilltop fortress where the stonework was vitrified (i.e. melted, apparently on purpose).

When I was a teenager reading LotR I always imagined that Weathertop was like the Tap O'Noth - it is quite a distinctly shaped hill (having a dirty great ancient fortress on top) and can be seen from a long way away.

That can be explained in a fantasy setting though. Arbitrary shapes of mountains can be attributed to ancient magic. Ancient elves and wizards might have been terraforming the geography for some reasons related to history of Middle-Earth.

The weird unnatural mountains around Sauron's area of the map might have been built by him using spells to create a "natural" protective wall from elves so he has enough time to forge the ring in secret.

If I remember correctly from the books (correct me if I am wrong), there is even a mention in the book about Misty Mountains being "built" by some ancient powerful beings (so that would explain ridiculous geology).

The Wall in Game of Thrones is also not natural, it was build using magic an is held together by the same spell that created it.

A great deal of the land west of the Misty Mountains was old Beleriand, which was the major battlefield of the War of Wrath between the Valar and Melkor (of which Sauron was merely a lieutenant to). As far as Mordor, I believe that the way those mountains are are as old as Time, since Shelob moved there sometime in the First Age after escaping from Ungoliant (her mother)

And don't forget that Middle-Earth was transfomrd from a flat world to a spherical one after the invasion of Valinor by Ar Pharazôn, which may have resulted in some deformation of the surface.

Also weren't there big stone giants living in Misty Mountains (even in the Hobbit movie there was a scene with them I think)? So that could explain a lot of inconsistent geology as stone giants could do a lot of "terraforming" during their battles. Over thousands of years they could have reshaped the original landscape.

I think you mean the Blue Mountains not Misty Mountains right? According to the map in the Silmarillion they were the Eastern border of Beleriand.

Of interest: Kirill Eskov's The Last Ringbearer. (https://en.wikipedia.org/wiki/The_Last_Ringbearer)

A retelling and continuation of parts of LotR, as told by a geologist rather than linguist. See also some of the author's commentary at http://ymarkov.livejournal.com/273409.html detailing some of Tolkien's geological mistakes.

You're in good company with some folks recently discussing this on SE:

https://scifi.stackexchange.com/questions/166884/plate-tecto...