a lot, obviously at front the template layout change that support layered replies, updating quote and reply comment
behind the scene, also change to how contents are pulled, threads are paginated, but in reddit style you may have 1st page comment with replies in 88th page
this can be overcome by adding additional column that map to a comment id
post per page will need to change, as you now might have some pages with more comments than other (altho this can be restricted by validating total comments pulled before ouput but then since replies are display in layer this will impact uniformity of each page
at this point might as well just do infinite scroll of post, accommodating new list with ajax request
and then maybe voting comment up, that's another can of worm (logically with current database structure we have to sort all posts linked to a thread first for that, this would slow down db operation a bit depending size
these are just some stuff i come up in few seconds, sure there gonna be more