Most of this is pretty technical and will appeal only to people who are already learning Sotah. Still, there are more general comments here and there.
Our mishnah lists chiddushim (novel lessons) introduced on the day R’ Elazar ben Azaryah took over from Rabban Gamliel in the beit midrash. It is not coincidental that R’ Yehoshua figures strongly in this mishnah – he was squelched at times by Rabban Gamliel, and one of those incidents was what led to R’ Elazar ben Azaryah taking over.
It’s interesting to see R’ Akiva involved in aggadata, non-legalistic gemara; at times (such as Sanhedrin 38b), sages rebuke him saying that he would be better off in legal analysis, saying כלך אצל נגעים ואהלות!
The use of לאמר on this page as “To repeat” is interesting. We have 3 other definitions for לאמר:
1) Tell this to others;
2) “Saying” (as in, “This was the message, saying…)
3) בדרך דרש, the gemara in Yoma 4b parses לאמר as לאו אמור, meaning, “Don’t repeat what you are told, unless you are told explicitly, ‘אמור Say it’.”
At the end of the mishnah, it appears that ירא אלקים is used to refer to fearing punishment rather than being in awe of Gd. [We’ll discuss this more, Gd-willing, on 31a when the gemara returns to the topic.]
At the top of the page: The gemara suggests that the Sotah water will not affect a woman unless her husband is innocent of sin. Rashi takes this as a sin related to her Sotah process – his having lived with her after the סתירה. Ramban, though, is broader, taking it as any sin of sexual impropriety.
The attempts at a קל וחומר logical argument are quite difficult here, from the perspective of logic. We compare food, which is a שני or שלישי or touched by a טבול יום and is therefore, itself, disqualified from use, with a person who is a טבול יום or מחוסר כפרה and there he disqualifies items he touches. The two are not really comparable. Further, in the argument on 29b to deduce from מחוסר כפרה to שלישי food, the fact that a מחוסר כפרה cannot eat from a קרבן is not because of טומאה, but rather it is from his ritual ineligibility due to the fact that he has not brought his קרבן!
It appears that they never answer R’ Yochanan’s question in this discussion.
Note that in the middle of the page our gemara plays an interesting switch, changing the way we define the numbers of ראשון, שני, שלישי. Instead of looking at them the normal way, as counting the distance from the original טמא entity, we now look at them by what they can generate – how many layers of טומאה can emanate from them.
The word לא at the start of the third line should be לאו to be Aramaically consistent.
See Tosafot מר on whether the law of Techum Shabbat is biblical, and what might be the source פסוק.
On the last line, the word עוברים should be עוברין to be Aramaically consistent.