Having upvote/downvote rather than support/report-fallacy would allow following interesting points more easily and burying trolls.

Including an "AND" premise would be useful in order to separate premises into smaller chunks. This is useful once cross-argument premise linking exists because it can be used to clarify logic and also to tease out contradictions.

Users need to follow arguments (not just other users).

Nicer keyboard shortcuts, like vim's hjkl for traversal would be cool

Being able to link premises to premises in other arguments. In this way a belief system can be detailed not just a single argument.

Notifications don't show when another user replies to my premises.

They should make premises split able.
Because often people make a true and a false statement in one premise.
And it would reduce infant mortality