Has this ever been mentioned as a weakness, or ever played against her?
Yes. Leela's lack of depth perception leads to many problems. In the first episode, it keeps her from catching Fry and Bender. In the episode, "A Clone of My Own", it keeps her from beating Cubert up (or however you spell his name). In the episode "A Leela for Her Own", her lack of depth perception causes her to become the worst Blernsball player in the history of Blernsball because she throws bean after bean after bean. Along with those three examples, there are many other situations where a second eye would have come in handy.
Yes. It's mentioned in the pilot (when, about to install Fry's career chip, she tells him, "Now hold still. I don't have very good depth perception"), and occasionally thereafter. For example, in the episode where the professor presents his clone Cubert, Cubert comments to Leela, "There's someone I'd like you to meet. His name is depth perception." When Leela tries to strike him angrily, she misses, and he comments, "Wow, that hurt . . . the air!"
In "A Leela Of Her Own" after a pickup blernsball game between the Planet Express team and the Cygnoid Pizza Shop Staff across from them (I think, season 4), Leela winds up being put in history books for all the wrong reasons.
Leela gets picked to be pitcher of picnic game. Thanks to her bad depth perception, She tosses the ball into the skulls of four Cygnoids - in a row (unwittingly digging her own team a bases-loaded-with-no-outs grave, and forcing the Papa Cygnoid to come to home plate and proclaim " YAY , I Make A ScorePoint!" ).
Despite doing what every pitcher shouldn't, she gets recruited by that Robot Fighting League boss to pitch as a mop-up / bullpen pitcher for the New New York Mets blernsball team he owns. Its obviously nothing but a 'Danica Patrick in Indycar+Nascar' Publicity Stunt since she'd be the first ever female pro-blernsball player.
In the majors, she picks up a huge female fanbase since, like her performance against Cygnoids, she also does nothing but throw the blernsball at the noggin of the boys on opposing teams.
While Leela was signing autographs she was introduced to Jackie Anderson (the only black collegiate blernsball female standout) who said Leela was robbing the spotlight of hers and other female blernsballers who get overshadowed by the tales of Leela's horrible pitching. The encounter encouraged Leela to not go down in history as the only blernsball pitcher to NOT RECORD AN OUT (and therefore, worst player in blernsball history and all of sport). So Leela seeks lessons, albeit, from the worst blernsball player in Hall of Fame , Hank Aaron XXIV .
Hank Aaron told Leela to overcome her miserable depth perception by urging her to toss her blern pitch WITHOUT LOOKING .
Leela's opportunity comes as her NNY Mets manager calls her into the game as they are in danger of losing their 8-5 lead in the final inning as Boston gets the bases loaded (Even with 2 outs and a ground-out to field, the clown at Second Base picks up blern AND tosses his whipped cream pie to first baseman INSTEAD OF THE BLERNSBALL. Only the METS !). Leela comes up to close the game out, she only needs to get the go-ahead run OUT- who turns out to be the newly drafted substitute/pinch-hitter, Jackie Anderson.
Leela shocks the crowd and because of her lessons with Hank Aaron, she gets in front of Anderson throwing two strikes without swing. But on the final strike, Anderson hits the blern making it break off the string, and that blern goes through the center of the bullseyed pinball board marked
" HIT IT HERE , AND WIN THE GAME "
Grand Slam Blern. Mets Lose Again. Leela blew the save chance and lost the game for Mets and still, having never gotten an opponent out by strike out ground out or fly out.
Hence Leela's likeness is placed in the Blernsball Hall of Fame replacing Hank Aaron as the worst blernsball player of all time, as an eternal trivia question answer.
Done in by her bad depth perception.
tl;dr Leela was a pitcher in a pickup blernsball game between her coworkers and the new Cygnoid neighbors but her bad depth perception causes her to toss every blern into the Cygnoid's heads, making her team pick another pitcher. Nevertheless The Boss OF New New York Mets invites Leela to play for his blernsball team as a self-destructing publicity stunt. Leela's lack of depth perception results in her not able to record an out as every player got struck in head by her rogue pitches. Ironically in Leela's final appearance the *second-ever female pro blernsball player hit a grand slam blern off her pitch.
Leela's horrible depth perception led to her having the status of the worst pro-blernsball player ever and the number 1 black-listed free-agent pitcher !
In the pilot she grabs for Fry but he moves away from her. She says to him, "Hold still damn it! I don't have good depth perception." In 'Fear of the Bot Planet', Leela can not watch a 3-D movie, because the 3-D glasses are meant for people with two eyes. In 'Cyber House Rules' it was revealed that Leela was picked on as a child for her eye. It also revels that she is used to applying her eye shadow as a straight line. Amy had to help fix it. Leela is also is seen throwing away a collection of monocles. She earned 'Worst Bleurnsball player' title because her depth perception was off and she kept hitting players in the head. In 'How Hermes Requisitioned his Groove Back' Leela sings 'They said I probably shouldn't fly with just one eye'. That's all I can remember from the top of my head, but I'm sure there are more.
Yes and no. It does in some episodes but is completely disregarded in others. This could mean that although it does affect her she has found ways to cope with it or she's just learned to live with it, although the only episodes where she said it affected her were ones where she was flying... perhaps it's just flying.