Some ideas:

The logical structure of an argument could be more clearly demonstrated by argument diagramming techniques.

Wherever possible, seek to replace intuition with explicit evidence.

Similarly, try to track the definitions of key concepts, ensuring that every term is fleshed out in more concrete terms, somewhere. Thus, issues of usage are replaced by pointers to specifics.

None of these are new ideas on LW, but they should ask help this goal.

Well, one important thing to avoid is the type of argument that requires massive exhaustive search through a vast space to find a flaw. It can be perhaps escaped by declaring such arguments void unless the full exhaustive search has been performed by a computer.

I had some thoughts for the models. An argument based on the imperfect model of real world should outline imperfections of the model and then propagate the imperfections along with the chain of reasoning, as to provide upper bound on the final error. It is often done with computer simulations of e.g. atmosphere, where you can e.g. run simulation a lot of times with different values that are within the error range and look at the spread of the outcome.

Use precise language, with explicit and/or clear definitions?

I admit that "Write better" is not often helpful advice, but it is good advice.