Pilot (aka Emotions in Motion) - S1-E1
Visible crew/equipment: In the scene outside of the Rialto, where Dawson is scolding Joey for being rude to Jen, Joey's shirt is falling off one shoulder. She shrugs to fix it, and her shirt lifts in the back, exposing her mic. (00:31:50)
Pilot (aka Emotions in Motion) - S1-E1
Visible crew/equipment: It's morning at Jen's and Grams'. Jen is seated at the kitchen table downstage/far left. Grams is upstage/right at the stove scrambling eggs. Grams crosses downstage to put the eggs in front of Jen and the mic overhead upstage/right peeks out just a tiny bit. Grams crosses back to the stove. Suddenly the microphone - including the rod the mic is on - just drops down almost completely into the frame over Grams' head and is not pulled back up.
Answer: It's only explained once in the series. Jack says to Andie "I tried to start kindergarten without you", meaning Andie was smart enough to start school early.