Be Patient, then Dash! - GOLD
Before reading other responses:
When Art forgot to return the Berserker to hand, he committed a Game Play Error - Missed Trigger. Since this trigger would usually be considered detrimental, he will receive a Warning.
Nin's actions seem a bit more problematic - Judges might assume that this constitutes cheating. However, players explicitly do not need to remind their opponents of their opponents' triggers - holding off on reminding Art is not an infraction, and it's not allowing an infraction to happen. Nin may be doing it intentionally, to gain an advantage, and it might be an angle-shoot, but it's not illegal. Nin has committed no infraction.
Now, the question is, what's the appropriate fix, now that the trigger has been remembered?
Dash creates a delayed trigger, that changes the zone of an object - it moves Lightning Berserker from battlefield to hand. The IPG instructs us that we will resolve this trigger, no matter the amount of time that has passed, and the opponent chooses whether the trigger will be resolved at the next priority, or at the next priority at the start of the next phase. Nin will almost certainly choose to have the trigger resolve immediately - the Berserker will be returned to hand before combat damage is dealt.
While this is the correct ruling, this is certainly going to be a feel-bad situation for Art, as it's a pretty big swing in advantage, due to a particular application of tournament rules. When explaining the ruling, we need to be sure to be sensitive and empathetic, and explain our reasoning clearly. I would try something like the following:
“As part of casting a creature for its Dash cost, you need to return the creature to your hand at the end of your turn. This trigger is an important part of how Dash works - even if you forget the trigger completely honestly and accidentally, forgetting to return the creature to your hand can give you a pretty big advantage. I believe you when you say that you missed this one accidentally. However, since it's a trigger that's usually considered detrimental - a.k.a, usually advantageous when forgotten, I'm going to assess a Warning. This Warning by itself is not a huge deal, just play carefully for the remainder of the tournament, don't forget any more Dash triggers, and you'll have no problem.
With regards to Nin - it's your responsibility, and only yours, to remember your triggers - your opponent doesn't have to point out when you forget your own trigger, though they certainly can choose to do so. Nin's actions are completely within the rules. That said, Nin, you should be aware that while this situation is working out as you expect, that won't necessarily always be the case when working near the edges of tournament rules, so you should understand that, in the future, a similar play may or may not work out to a similar advantage. If you ever have a question about the legality of reminding, or not reminding, you opponent - just call a judge and ask to speak away from the table.
Now as for the fix - at this point, your opponent has reminded you of the trigger that you forgot. Because of the type of trigger it is - a trigger that moves a card from where it is to somewhere else, the prescribed fix is to resolve the trigger now. So, before we move to combat damage, we'll be returning Lightning Berserker to your hand.
I'm applying a time extension of <x>, please play carefully, and continue the game”.
After reading other responses:
There is a surprising amount of consensus for a Gold scenario. I must be missing something. :P