Letter forms
A scribe today has an exhaustive list of rules for how each letter ought to look – here’s an example for letter shin, from the Mishnah Berurah:
Shin has three heads. The first head, with the leg which is drawn out of it, is like a vav, and its face is tilted slightly upwards. The second head is like yud; its head is tilted slightly upwards, and ideally it has a little prickle on it. The third head must be made like zayin, and it has three taggin on it. The left heads of all the letters שעטנז גץ are like zayin. One must take care that the heads do not touch each other. The leg of this left head should lekhathilah be particularly vertical…
and it goes on, I won’t give you all of it here.
Specifically, it’s interesting that the later authorities – i.e. the ahronim, post-Shulhan-Arukh, more or less – devote a lot of space to defining how the letters should look, but the rishonim and earlier (including the Shulhan Arukh) don’t seem too interested in that – they know how the letters ought to look, and they content themselves with reminding you particular ways in which you ought not to stray, like not making alefs ayins and suchlike.
Alef-bets differ with region and period. We’ve already seen some of the ways Ashkenazic and Sephardic alef-bets differ, when we were discussing influence of writing implement on letter style. We didn’t discuss there how those styles relate to the laid-down rules for letter forms.
Letter shin is a case in point. Literally.

Sephardi shin

Ashkenazi shin
Shin, for Ashkenazim, has to have a pointy bottom. But Sephardim don’t necessarily agree with that, and many Sephardi styles give shin a rounded or flat bottom. Now, most Ashkenazim don’t think that this is a deal-breaker; you can still recognise the letter as shin, after all, but a few Ashkenazim do think it’s very much a deal-breaker. They may even avoid Torah readings from a Sephardi-style Torah on this basis. Some Sephardi scribes add a nominal point to their shins, as here, for compatability:

This is a formalised example of how minor variation in letter forms can affect how kosher it is – formalised because the variation is accepted as valid by different branches of the tradition. Accidental variation is more likely for the sort of proofreading I’m doing.
Mirrored from hasoferet.com.
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The Teimani style as reported by Rav Qapah has a small point and I really doubt it's because they care in the slightest what Ashkenazim think. I've looked over a few Sepharadi styles and while you're right that often newer, mainstream Sepharadi writing will make concessions to Ashkenazim (ex. Rabeinu Tam's yodh), there are many many older hands with the point in the shin. There's no reason to suppose that is in essence an Ashkenazi thing.
Shavua tov (from the perspective of Jerusalem).
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מסכת שבת קד ע"ב:
שיקרא אחדא כרעיה קאי
רש"י:
כל אות ואות שבו עומדת על רגל אחד
Standing on one leg could conceivably include an interpretation with a rounded bottom (b/c it's clearly not TWO legs, the main point of contrast here with the word אמת), but it takes fewer mental gymnastics to fit the description to something a wee bit pointy.
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Not that there aren't differences, just that they aren't as exaggerated as they can be today, and as you'll see if you look there are examples of much more rounded Ashkenazi shins.
Anyway, about what completely-rounded people say about the Gemara excerpt. I think they would simply interpret it to work for them, namely, say that a rounded line like that does indeed rest on a single point when it comes down to it, unlike the solid bottom of, say, a mem sofith.