One discourse norm that I think is really important is that of having to either support or retract accusations if challenged. If you say something negative about another person, their work, etc. and they ask you to explain yourself, I believe you are compelled to either justify or retract your statement. This creates a strong barrier against unjustified attacks and gossip, while still allowing justified criticism.
Here are some examples of what this norm might look like in action:
1. Alice posts about her thoughts on an issue; Bob, who dislikes Alice, responds with snarky insults about Alice's motivations. Alice asks Bob to explain his accusations, and he doesn't do so or replies with more insults. Moderation intervenes against Bob.
2. Carol posts a brief comment saying a project is incompetent. Darryl replies asking her to provide more detail or retract. Carol links to a post that explains her critique in more detail.
3. Efren posts a statement criticizing an event that will soon be held. Faye asks Efren to back up his criticisms. Efren decides that his claim was actually more emotional and less grounded than he first thought, so he decides to retract his original statement.
Now, someone might ask "why try to make it more difficult to be critical of something?" The answer is that making fun of things is easy [1], and in general norms online often trend too much in the direction of low-content mockery rather than reasoned debate. Holding norms that require people to back up or retract controversial statements can be a good step away from that failure mode.
[1] Full disclosure: I wrote the linked post under my old username.
For in-person conversations (I know this was meant as a norm for public discourse): Personally I tend to have a hard time digging into my memories for "data points" when I have a negative or positive impression of some person. It's kind of the same thing with people asking you "What have you been working on the past week?" – I basically never remember anything immediately (even though I do work on stuff). This creates asymmetric incentives where it's easier to make negative judgments seem unjustified or at least costly to bring up, which can contribute to a culture where justified critical opinions almost never reach enough of a consensus to change something. I definitely think there should be norms similar to the one described in the post, but I also think that there are situations (e.g., if a person has a reliable track record or if they promise to write a paragraph with some bullet points later on once they had time to introspect) were the norm should be less strict than "back the judgment up immediately or retract it." And okay, probably one can manage to say a few words even on the spot because introspection is not that slow and opaque, but my point is simply that "This sounds unconvincing" is just as cheap a thing to say as cheap criticism, and the balance should be somewhere in between. So maybe instead of "justify" the norm should say something like "gesture at the type of reasons," and that should be the bare minimum and more transparency is often preferable. (Another point is that introspecting on intuitive judgments helps refine them, so that's something that people should do occasionally even if they aren't being put on the spot to back something up.)
Needless to say, lax norms around this can be terrible in social environments where some people tend to talk too negatively about others and where the charitable voices are less frequent, so I think it's one of those things where the same type of advice can sometimes be really good, and other times can be absolutely terrible.