During the blackout in the apartment when Phoebe, Joey, and Monica are talking, Phoebe lets slip that Monica had a crush on Joey when he was first moving in and Joey didn't know about it. However, in the episode The One with the Flashback (1996) in season three, Monica flirts with Joey and invites him in for lemonade, and Joey takes it as an invite for sex, and strips down naked in the apartment while Monica pours the drinks.
Joey says that the weirdest place he has ever had sex is the women's room on the second floor of the New York City public library. However, the bathrooms in the NYC public library are located only on the third floor.
The magnetic locks on bank vestibules do not engage during a blackout or a fire alarm for the very reason of not trapping people inside.
When Joey brings in the candles, he says Chandler's old roommate was Jewish and that is why he has the menorah, but the menorah only has 7 candles, while a Hanukkah menorah has 9. However, Joey is not Jewish so he wouldn't know the difference between the two.
Just as the episode starts after the intro, the first thing Monica does in a blackout, is making a call with her mother on a corded landline telephone. Corded landline phones will work during a blackout because the phones get their power through the phone lines from the telephone network.
When Chandler is choking on gum in the ATM vestibule, you can clearly see the actor Matthew Perry is storing the gum in the right side of his mouth so that he can spit it in a later shot.
When Joey blows out the last candle, the flame is extinguished several seconds before the room becomes dark, revealing that the studio lights and not the candle are creating the candlelight effect.
When the girls knock on Heckles' door to ask if he's the owner of the cat, they are acting as if they have never met him before. His character doesn't even have a name at this point. However, in "The One with the Flashback," which took place before this episode, Heckles is complaining about the noise that he thinks the girls are making, and the girls clearly know who he is.
When Phoebe is counting down the last candle's burn and Joey blows it out, the sound of his breath is heard several seconds after he blows the candle out.
When Phoebe is making up a song, she talks about the milk getting sour and how she stays away from dairy anyway. In The One with the Dozen Lasagnas (1995), Rachel asks for milk and Phoebe has some in her bag despite staying away from dairy. However, it may simply be that Phoebe has changed her stance by then.