It's a very literal interpretation that "the Dark Side" literally hinders the Jedi's clairvoyance.
Luke and Anakin are both berated by Yoda for not being in the moment, for not looking at the present, and thus missing what's in front of them. I think there's an explanation for that in the Jedi Code with these two lines:
There is no emotion, there is peace.
There is no passion, there is serenity.
Emotion and passion lead to the Dark Side (whatever that is) according to the Jedi, but the important part here is the Code opposes emotion and passion to peace and serenity. Emotions cloud your judgement. It is a Jedi teaching, but it's also a real-life human thing that you certainly have experience with. It seems to me that, according to the Jedi, clairvoyance come to those we can let go of their emotions, reach a dispassionate state, and don't wander off thinking about the past or the future (what you might otherwise call being distracted). You need to reach a meditative state of sort.
You don't need training to reach that state. Luke takes a deep breath and calms his mind in the cockpit of his X-Wing to sense the exact moment he needs to fire the proton torpedoes. To sense the future however seems to require a much higher threshold of meditation, one that can elude even Yoda.
I would interpret the "Dark Side" here as those fears and angers you might experience by trying to look ahead into the future, and having those emotions derail your vision. Clairvoyance is thus clouded by the Jedi's emotions rather than by a literal Dark Side.
But what about the Sith? Well, the Sith Code have a different philosophy.
Peace is a lie. There is only passion.
Through passion I gain strength.
A core tenet of the Sith teaching is use your emotions, mainly shown as anger and fear. There is some human truth to that too, but as a philosophical teaching, the Sith's pursuit of power would necessarily put them in the opposite of a meditative state, in a state of constant anger, fear, greed, and all those things the Jedi warn you about. That also means that, if there's any truth to the Jedi's teachings, the Sith are blinded by their own emotions, just like the Jedi are. After all, the Force works the same for everybody, doesn't it?
Palpatine talks of "foreseeing", but it's unclear whether that's meant to be literal or a manner of speaking. Due to his station and to the Sith's rule of two, he certainly can't appear weak, and flaunting the ability to see the future is certainly good for prestige. But that doesn't indicate whether that's an actual ability he has or not, nor how it's supposed to work.
What we do know is he made the attack happen. He leaked the plans, he made the Death Star II a target too good to pass, trying to lure the Rebel Fleet into a trap. That's not foreseeing, that's planning. The things he doesn't foresee and end up being his downfall can be chalked up to overconfidence, a complex of superiority, a general lack of strategic planning, or other human shortcomings. His plan simply wasn't as foolproof as he thought.
Someone with a calmer mind might have been able to look back at his plans and find the obvious weaknesses in it. If he used a Force ability, then it's obvious it doesn't give a full picture, or that he wasn't powerful/clairvoyant enough to see or interpret it correctly. But I think it's more likely to be a matter of "the Dark Side" clouding his judgement as well.
Because in the end, we see Palpatine being guilty of the same things Yoda berates Luke and Anakin about. He's so far up his own ego, thinking he's won, maybe thinking about the future of his Empire, focused on Luke's incoming death, that he doesn't sense Vader's thoughts turn to the Light. He didn't see what was, in fine, in front of him.