I’m going to an express a contrarian view to this question (most movie fans will scream “OF COURSE YOU MUST”):
It depends.
Do you like black and white movies? Can you pay attention to a movie that does not have explosions? Do you appreciate a good story? Do you love film? If you answered No to more than one of these questions then… No, you should not watch Citizen Kane.
As much as I LOVE Kane, I also love many things that modern audiences has simply never cared for. Whether this is be just loving things that are dated and no longer relevant, or people have lost all sense of what good entertainment is – well, it doesn’t matter. There is a reason Vertigo has surpassed Kane as the “best film” in many polls – it is more modern, more filled with angst and pathos, and about obsession and sex. In other words – it’s a more “relevant” film to today’s audiences than Kane.
It’s almost a question that answers itself. If you have to ask, well – there’s doubt. You are coming from a place of skepticism, not hope or interest. With that (even slight) prejudgement, you may not like Citizen Kane. You’d be completely wrong, but it’s your choice and your life: enjoy that Absolute Wrongness.