"At any rate, it is safer to leave people to their own devices on such subjects. Everybody likes to go their own way – to choose their own time and manner of devotion. The obligation of attendance, the formality, the restraint, the length of time – altogether it is a formidable thing, and what nobody likes." (9.15)
Though Mary is commenting on church services and how boring they are, she's also expressing an interesting philosophy of tolerance. Mary believes in letting people do their own thing, whatever that may be. This greatly contrasts with Edmund and Fanny, who each have much stricter senses of how people should behave.
"I speak what appears to me the general opinion; and where an opinion is general, it is usually correct." (11.24)
Mary is being witty, but her thoughts on the "general opinion" are revealing. Mary doesn't see anything wrong with society at large and seems happy to belong to the majority – the popular crowd and popular morality, in other words.
"Don't imagine that nobody in this house can see or judge but yourself. Don't act yourself, if you do not like it, but don't expect to govern everybody else." (13.32)
Tom scolds Edmund here for trying to boss everyone around. Edmund wants everyone to respect his (moral) authority. Tom, like Mary, embraces a much more open moral philosophy that lets people judge for themselves and do what they want.
[S]he had begun to feel undecided as to what she ought to do; and as she walked round the room her doubts were increasing. Was she right in refusing what was so warmly asked, so strongly wished for? (16.3)
Fanny worries about what she "ought to do" throughout the book and is kind of obsessed with doing the right thing and behaving correctly. But Fanny often has trouble deciding what the "right thing" is: is it a universal principle, good in any situation? Or does the "right thing" change with each situation?
It was, indeed, a triumphant day to Mr. Bertram and Maria. Such a victory over Edmund's discretion had been beyond their hopes, and was most delightful. [...] he was to act, and he was driven to it by the force of selfish inclination only. Edmund had descended from that moral elevation which he had maintained before, and they were both as much the better as the happier for the descent. (17.1)
Edmund often moralizes and his siblings are thrilled to find a crack in his armor, so to speak. Though Edmund rationalizes his decision to act as still "moral," his siblings are happy (in a rather mean way) to find that he's really no better than they are.
"The nonsense and folly of people's stepping out of their rank and trying to appear above themselves makes me think it right to give you a hint, Fanny, now that you are going into company without any of us; and I do beseech and entreat you not to be putting yourself forward, and talking and giving your opinion as if you were one of your cousins." (23.32)
Mrs. Norris's guiding principle in life seems to be the mistreatment of Fanny, specifically, and just being as unpleasant as humanly possible more generally. Her thoughts on social "rank," though, are actually quite common for the time period.
"Will [Henry] not feel this?" thought Fanny. "No, he can feel nothing as he ought." (23.67)
Fanny's sense of right and wrong even extends to people's personal feelings, as well as their ideas and their actions. Her very strict view of how people "ought" to be means that she frequently disapproves of just about everyone around her, except for Edmund, who has been instrumental in shaping Fanny's thoughts and opinions.
[B]ut she trusted, in the first place, that she had done right, that her judgment had not misled her; for the purity of her intentions she could answer [...]. (32.57)
One of Fanny's guiding principles seems to be a strong belief in her own "purity." Is she justified in this self-confidence, or does it lead her to arrogance?
She had all the heroism of principle, and was determined to do her duty; but having also many of the feelings of youth and nature, let her not be much wondered at, after making all these good resolutions on the side of self-government, she seized the scrap of paper on which Edmund had begun writing to her, as a treasure beyond all her hopes [...]. (27.19)
It's interesting that Fanny's principles are described as "heroic" here. The term heroism can be taken a couple of ways here. It can be read as sincere – the narrator may really be praising Fanny for sticking to her guns and doing what she thinks is right. Heroism can also be taken ironically, or humorously, though. Despite her overblown sense of her own principles, Fanny is still just a teenager with a massive crush, and often acts accordingly.
"[B]ut the manner in which she spoke of the crime itself, giving it every reproach but the right, considering its ill consequences only as they were to be braved or overborne by a defiance of decency and impudence in wrong; and, last of all, and above all, recommending to us a compliance, a compromise, an acquiescence, in the continuance of the sin [...]." (47.30)
Edmund's style of speech here is reminiscent of a sermon, which is appropriate given his job as a clergyman. Edmund has a rhythm here, the kind found in speeches (or sermons) in which the speaker is building up to big statement. It's easy to picture him saying this from a pulpit rather than in a drawing room with only Fanny for an audience.
I only entreat everybody to believe that exactly at the time when it was quite natural that it should be so, and not a week earlier, Edmund did cease to care about Miss Crawford, and became as anxious to marry Fanny as Fanny herself could desire. (48.24)
It's really significant that the narrator deliberately withholds the timeframe in which Edmund fell for Fanny. Basically, the narrator is implying that Edmund and Fanny can do no wrong, and people can figure out the timeframe themselves in order to make it "right" and moral. Edmund and Fanny can literally do no wrong – the novel is built on the fact that these two are always right.