In my work planner, it's usually not a mistake, but something that gets canceled or rescheduled. I have stickers that say 'canceled' that I put over the event.

For my bullet journal, it depends in the extent of the mistake. Small ones - correction tape. Bigger ones - I cut a piece from the back of previous journals the size of the mistake and glue it over the problem areas. Huge ones - I usually glue the two pages together and just skip right over them. I guess the alternative would be to cut the problem page out, but I worry about messing with the binding on the page it matches. Another option I've used it to switch whatever I was doing to white on black and just color over the mistake with a opaque black marker.