CONTINUOUS as a slug descriptor is useful if the space in which the scene is filmed has discrete locations where the action is shot. But you have to weigh against that giving the location its own description.
In the case of an apartment where the kitchen is visible to the living room, it would be appropriate. While a kitchen as a distinct room, you'd probably opt to give a separate slugline.
Using more/continued for scenes that carry over has gone away. However, it is still helpful--at least to me as a reader--to see when a character's dialogue extends to the next page. If reserved for characters, it happens fairly rarely. I would not ding a script for that but readers' tastes vary.