After Gilligan loses his glasses while playing on stage with the Professor, Mr. Howell and the Skipper as The Gnats, his glasses are back on in one scene before their song ends.
The small helicopter seen at the beginning of the episode couldn't possibly have carried all the band members and their instruments. It clearly had only two seats and no space for luggage.
When the Skipper, Gilligan, and Mr. Howell come across the band they are led to the band's location by the sound of the music. Yet the helicopter has flown in, dropped them off, and is spinning up to lift off. No way that the sound of the music (especially unplugged) would have drowned out a helicopter, no matter how small.
The Mosquitoes are able to play their electric guitars without amplifiers or electricity.
When Gilligan opens up the record album gift from the Mosquitoes, he bends the box to get the wrapping paper off, indicating the gift does not contain a record at all, just an empty box.
To tolerate sitting through the Mosquitoes concert, Mr Howell puts earplugs in his ears. After the group finishes singing--and leaves the stage and the area--Mr Howell continues smiling agreeably and glancing around, as he had throughout the concert. Mrs Howell pokes him and tells him to take the earplugs out because, "the concert's over, dear." His EARS were plugged, not his EYES.
When Mrs. Howell is singing with the Honey Bees, you can see the reflection of a few spotlights on her giant bee pin.
The women are wearing 'mod' clothes, such as white go-go boots and the white hat Mary Ann wears. But these were not in style yet when the Minnow was shipwrecked. The castaways don't have television, newspapers, or anything else that can give them a visual account of contemporary styles. The women not only couldn't know about mod clothes, but they couldn't have packed them either.
When the Honeybees finish their song, Maryann, Ginger and Mrs. Howell are all supposed to make a buzzing sound with their mouths.
Yet Mrs. Howell makes a puckering kissing motion with her lips before she realizes her mistake and makes the buzzing sound like Ginger and Maryann are making.