I found this quite difficult to work with. I believe that the moment you have a mundane task in a game you've failed as a designer and the game itself is flawed, mundane tasks if they were to appear should only be there for the players who enjoy the reward on the other end (players who like to 100% a game, kill all monsters, collect all items, fully customise their guns, etc).
I'll pick one thing that might piss people off; cut-scenes.
I wrote a crap load about delivering story at a good pace, I'm going to delete that and focus on one thing; optional story.
Player is walking around, they see something interesting, press the action key then suddenly they have 5 minutes of people talking about the subject of interest and you've wasted the player's time without warning, or worse yet you've made them advanced the story by accident when they weren't ready.
Design around this; if it's so interesting then make the player become curious about it. Have NPCs gathered around the object having their discussion around it, the player could sit about and listen to what they are discussion, if they are very interested they can get closer, trigger a more in-depth discussion with the player character involved.
If the player is in a hurry (speed-running) they can just run past the scene entirely.
Too many games feed information about the world via textual logs (newspaper clippings) or including them in critical scenes. If a game opens up telling me the 100 year history of the country it is set in then the game has failed, that information should be optional and delivered by making the player curious, not by forcing it on them (making them mash the continue button).
EDIT: And you have some people who think that dialogue trees and making characters move about every 8 lines is a way to make it less mundane. It's just something to slow it down. If you want a dialogue tree it should be the first thing that appears, not appearing half-way through a dialogue sequence that you've potentially been mashing through so picked up zero of what is going on.
EDIT2: Oh and the standard tactic for making these less mundane; QTEs! Here's some boring text, watch out because suddenly a rock is flying at you and you need to dodge it, good job here's more dialogue >:C