Why do women clap during prayer when the imam makes a mistake?
A brief clap draws less attention than a woman's voice in the middle of the prayer. Here Islam chooses the lesser evil so that the devotion of all worshippers stays protected.
It is true that Islam rejects clapping in worship. What is meant is clapping as an expression of joy or rapture, as is customary in some religions. Islam wants people to express their devotion in meaningful words that turn the heart towards God.
Sometimes, however, two principles meet. Then the principle of the lesser evil applies, which the Holy Qur’an itself recognises, as the first verse above shows. Clapping during the prayer is a good example. Here it does not express joy. It is only a brief signal to the imam.
On the other side stands a woman's voice speaking aloud into the silence of the prayer. Not all worshippers are equally steady. Some have not yet learned to control their emotions well, and a woman's voice could send their thoughts in the wrong direction. This does not apply to everyone, but every society has people with diseased hearts, as the second verse says.
A short clap, by contrast, is inconspicuous. No one can tell which woman it was, and the devotion of the others stays protected. So of two solutions the milder one is chosen.
This reasoning is an explanation of the wisdom behind the rule. Where the wisdom of a command is not stated explicitly, one may reflect on it. Anyone who finds a more convincing explanation is welcome to share it. The rule itself stands firm through the word of the Holy Prophet (saw).