Continuity mistake: When The Bride rubs off the name "Bill" written on the window condensation, the writing style is different from when it was first written by the sword maker. (00:52:45 - 00:53:30)
Continuity mistake: When Hattori Hanzo gives The Bride her sword, his assistant is sitting behind him in a cross-legged position. But the direction the assistant is facing keeps changing. (00:55:40)
Continuity mistake: When Hanzo hands over the sword to The Bride we can see all of her hair is hanging down on her back. When it cuts a huge lump of her fringe hangs in front of her. (00:55:55)
Continuity mistake: When Boss Tanaka breaks the bowl on the table, a piece of meatball rolls on the table. Later when the other Japanese guy throws a hand towel on Tanaka the meatball is gone. (00:59:00 - 00:59:45)
Continuity mistake: When O-Ren chops off boss Tanaka's head, the head falls in front of Sophie and another member. Then, when O-Ren finishes her speech, she holds up Tanaka's head. This can not be possible, because she has not moved from where she was standing during the speech. (01:00:20 - 01:01:30)
Continuity mistake: After cutting off Boss Tanaka's head, O-Ren whips some of the blood on her sword onto another boss' face. He jerks his head back with specks of blood on his face, but just a split second later in a different shot his head is still and there is no blood at all. (01:00:25)
Continuity mistake: After O-Ren chops off Tanaka's head at the Yakuza boss meeting, the position of her hand holding the sword changes. At first she is holding it with an overhand grip, then when the blood shower from Tanaka's neck ends, she lowers the sword and is gripping it underhand. (01:01:30)
Continuity mistake: When The Bride cuts Sophie's arm off you see her get covered with blood. In the next shot, however, there is considerably less blood on her top and it is in a different pattern. (01:11:20)
Continuity mistake: When O-Ren Ishi tells 'Charlie Brown' to get lost we see some blood stains on The Bride's face. The stains differ in the next few shots of her, then later when we get a close-up of her face the blood stains are the same as earlier. (01:12:00)
Continuity mistake: The Bride raises her sword twice at the beginning of the fight with Gogo. (01:14:55)
Continuity mistake: When the bride is holding a table, GoGo throws the mace ball at it. She then pulls the mace ball back through it. The table splits in two. The piece of table that falls at the bottom of the screen, the bride's right hand side, falls completely apart. The legs have broken away from the table top. In the next shot this piece of table is standing on end with the legs reattached. (01:18:55)
Continuity mistake: The table that Gogo falls on after hitting herself with the mace gets splintered into pieces, with debris underneath and all around where she lies on her back, especially in the area below her feet. Yet in the next shot when the Bride jumps down to resume her attack from above, there is no sign of the debris on the floor. (01:20:00)
Continuity mistake: During the fight in the restaurant, the Bride is surrounded by a large group of Yakuza. In a shot from behind her, she is staring at the opponents in front of her over the edge of her horizontally held blade. One of the masked villains is swinging a chain in an arc. A moment later the shot cuts to an overhead and the guy with the chain has disappeared - everyone in front of the bride (as well as to the rear and sides) are holding swords. (01:22:30)
Continuity mistake: When The Bride is fighting the Crazy 88s, right after it changes from black/white screen to color again, they fight in a room where the light gets shut off. Now watch close, they wait. They fight. She hits a few members of the gang. Watch the gangster in the lower left corner of your screen. He's gone. He rolls away to the left. They start fighting again. Keep paying attention to the lower left corner. You see him roll away again a few seconds later. (01:27:25)
Continuity mistake: This error only occurs in the Japan version: Here, the little boy (the only one who doesn't wear a mask) "The Bride" fights before confronting the head general of the Crazy 88 had already fought against her in the middle of the battle with the rest of the gang. In that short fight she cut his mask off (explanation why he doesn't wear it at the end), realised he was only a child and then instead of killing him threw him into one of the pools. You actually see him falling into the water. But at the end when they meet again, he is completely dry (except for his sweat). (01:28:35)
Continuity mistake: When The Bride is slashed on the upper back by O-Ren in their fight scene she collapses and lands on her back in the snow. After she gets up and the fight continues, there is no blood spot on the snow where she was lying. (01:29:55 - 01:31:10)
Continuity mistake: When O-Ren takes off her sandals to fight the bride she pushes her right sandal out from under her. It slides on top of the snow and does not push around a lot of snow. No snow collects around it. In the next shot when she takes off her left sandal, the right sandal now has a lot of snow that was pushed up around the side of the sandal and collected beside it. It is also sunk much deeper into the snow than in the previous shot. (01:31:35)
Continuity mistake: At the beginning of the fight between Oren and the Bride in the garden, Oren puts the sword up to eye level and starts to withdraw the blade from the scabbard. The shot switches to a view from behind her and we see the back of her head. The eye-level sword, however, is nowhere to be seen. When the shot switches back to Oren's face, the sword has reappeared. (01:32:20)
Continuity mistake: When O-Ren falls dead in the snow, only the snow by her feet is pushed up. In the next overhead shot there are big footprints/marks in the snow near her legs, and her samurai sword has also moved. (01:33:35)
Continuity mistake: As The Bride writes her "Death List Five" on the plane, the handwriting of everything greatly changes between shots. (01:38:15)
Answer: From what I understand the reason for the lights being off is the same reason for why the previous scene was done in black and white; to decrease the amount of 'graphic violence' in the movie in an attempt to keep an 'R' rating. I would assume that they had him shut off the lights for that scene as just another method to accomplish that task.
I believe the original question was asking why was it done within the context of the film (i.e. why did the character shut off the lights) not why was it done in reality. My best guess is that the manager switched off the lights thinking the 88 had a better chance of killing the bride if she couldn't see. True, they couldn't see either but there were so many of them one could possibly have gotten to her.