What is the ruling regarding someone (whether male or female) correcting the imam of the salah if they are not praying behind him. Is this permissible?
Yes it is permissible for the one who is not praying to correct the one who is praying. (This is) based on the hadith of Anas ibn Malik when the companion came from praying with the Prophet (peace be upon him) and the qiblah was changed. And he found a group of companions still praying towards baytul maqdis. (As a result) he corrected their direction while they were praying. As for a woman, she may also correct a man if he is praying. And if he is not from her mahram, she must not be soft in speech as Allah says:
إِنِ اتَّقَيْتُنَّ فَلَا تَخْضَعْنَ بِالْقَوْلِ فَيَطْمَعَ الَّذِي فِي قَلْبِهِ مَرَضٌ وَقُلْنَ قَوْلًا مَّعْرُوفًا
If you fear Allah , then do not be soft in speech [to men], lest he in whose heart is disease should covet, but speak with appropriate speech.
It also falls under the way of cooperating with one another upon good and rightness as Allah had commanded:
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment
~ Abu Aisha Yassin