1. See ר"ן who points out that a צורת הפתח is mentioned by רבא as a possible requirement for the third wall if you are using only the טפח of the הלכה למשה מסיני for your wall. The ר"ן proves from here that a צורת הפתח will NOT help for the other two walls, even though they DO work for שבת. If this weren’t true, then there would be nothing special about the third wall if it needed a צורת הפתח as well. This would mean, of course, that סוכה in some ways is more חמור than שבת. The ר"ן explains that this point is part of a סוכה needing מחיצות הניכרות. However, see the פּני יהושע who is addressing the question asked on the רי"ף as to why the רי"ף doesn’t mention that רבה’s statement, “a סוכה’s walls that are valid for שבת are also valid for סוכה” is only on the שבת of סוכות itself, but not during the week. He answers that the רי"ף held that since at the end of the גמרא we say השתא מקילתא לחמירתא - אמרינן, מחמירתא לקילתא - לא כל שכן, it turns out that a מיגו is not necessary, and we really are learning it from a קל וחומר, and therefore it is permitted to use the סוכה even during the week. Based on what the ר"ן is suggesting, this would seem to be difficult since there are things which are valid on סוכות and not on שבת (without the פּני יהושע, the simple reading of the גמרא is aקל וחומר in regards to the concept of מיגו which would be a good קל וחומר).
  1. The גמרא states that the טפח must be a טפח שוחק. The ר"ן asks why a regular טפח isn’t valid as it would still equal more than 50% of the minimum wall (it would be 3.9 טפחים or so). He answers that what one really needs is a מקום חשוב and that can’t be less than 4 טפחים. Theערוך לנר asks a fascinating question on this: why isn’t רוב enough? Don’t we always says רובו ככולו? The חתם סופר (OC: 141) answers that there is no רובו ככולו when there is no כולו. Meaning, if there are 10 people and 7 haven’t said ברכו, then we can say they have a minyan. But if there are only seven people, then there is no minyan. Similarly, רובו ככולו cannot create the כולו when there is a shortage of what is necessary. It can only make the מיעוט go after the רוב.
  1. See the ריטב"א who says that even though the גמרא says that one need a פּס of 4 טפחים and a משהו for a סוכה that is a מבוי, if the two walls of the מבוי are 7x7 (minimum size of a סוכה), then if one put the regular שוחק טפח in the middle, we should apply לבוד to both sides and the סוכה should have been כשר without the פּס. However, he says that this is not the case since a סוכה requires at least two walls to be truly connecting if you want to avoid a פּס of 4 טפחים. See the ערוך לנר who discusses this and says it’s a מחלוקת ראשונים.

4.  The רי"ף brings the halacha that פּסי ביראות are good for a סוכה since it is good for שבת . The ר"ן asks that since the רי"ף only bring things that are relevant today, why did he bring this? פּסי ביראות are only a היתר for the עולי רגלים ‘s animals? He answers (like תוספות says on his own) that what is meant here is that anyone who makes walls similar to פּסי ביראות can use them as walls of a סוכה, since we find they were lenient by עולי רגלים (meaning מדאורייתא it is a רשות היחיד), they would also be lenient to allow you to perform this mitzvah. However, the ר"ן does not like this idea since it means that the halacha ofפּסי ביראות has nothing to do with the מיגו. If so, it should not have been compared to halacha ofסיכך על גבי מבוי. What comes out of the ר"ן and תוספות is another point—there is a disagreement as to whether the case of סיכך על גבי מבוי would be valid during the week where it is not שבת and no מיגו is functioning. According to this, everyone would agree that פּסי ביראות are good the whole week of סוכות.