Revealing mistake: In the scene near the beginning where Leela tells Fry and Bender to watch the political debate on television, both of them (Fry and Bender) fall asleep. When Leela "hops" on the couch to wake them up, Bender's arm, despite being behind Leela, can be seen through her white shirt for a few frames.
A Bicyclops Built for Two - S2-E13
Revealing mistake: At the end of the wooing near the end, you can see that Fry has four arms.
Answer: You are thinking about episode 20 of series 2 - "Anthology of Interest I". She technically never kills anyone, but in the episode she ask a "What if machine" (one of the Professor's inventions) what would happen if she was more impulsive. The machine then shows the more impulsive Leela killing off the Professor to get the money from his will and thereafter killing Hermes, Bender, Scruffy, Cubert, Nibler, Amy and Zoidberg to cover it up. Finally she does something really impulsive with Fry.
Andreas[DK]