Director Hayao Miyazaki performs a Creator Cameo for a moment in the scene when the street-sweeper says "That's my broom she used". He's in the upper-right corner of the picture.
The fact that Kiki uses some random broom in order to rush to save Tombo. She never does bring it back like she promised though.
Either that or she did bring it back, and he let her keep it.
The climax of Kiki's Delivery Service when Kiki sees her friend, Tombo, in deadly danger in a airship accident and knows she is the only one who could save him, if only she can fly. Desperately, she finds that inspiration her artist friend said she needs and grabs a laborer's pushbroom for a focus for her flying. The scene goes silent at Kiki concentrates to reclaim the magic she lost until the broom's bristles suddenly bursts, a circling wind gathers around her until she quietly gives the command, "Fly!" At that moment, she rockets up into the air to save her friend.
Kiki's takeoff on the borrowed broom is a crowning moment of awesome for Miyazaki too as it is arguably the best sequence of hand-drawn animation ever put on film.