Tyrion points out that many innocent people would be killed, unless Jaime persuades Cersei to surrender; Jaime replies that he never really cared for them. However, Jaime killed Aerys in order to save the same innocent people, and he also joined the fight against the army of the dead because he promised "to fight for the living."
Cersei says: "The Red Keep has never fallen"; actually, it previously fell during Robert's Rebellion, by the Lannister army.
Arya and the Hound left Winterfell in the previous episode The Last of the Starks (2019) before the Northern army. They are supposed to travel much faster (as opposed to an army with thousand of soldiers and provisions, etc.) and they have no motivation to linger anywhere. Yet they arrive after the Northern army has reached King's Landing and established a siege perimeter.
Tyrion states that "if the city surrenders, they'll ring the bells and raise the gates," yet in Blackwater (2012), Davos states "I've never known bells to mean surrender," and Lord Varys also says the bells ring for "a city under siege," disproving that bells signal Kings Landing's surrender, and subsequently the title of the episode itself.
Tyrion says there are a million people in King's Landing; in The Bear and the Maiden Fair (2013), Jaime said that the population of King's Landing at the time of Robert's Rebellion was 500,000. The city population could have grown during the two decades that passed since Robert's Rebellion, but it couldn't possibly double.
In the scene with Varys' execution (final appearance of Conleth Hill), take into consideration the size of fire-breathing dragon Drogon. Varys stands there, Daenerys sentences him to death, Tyrion, Jon, Grey Worm and soldiers stand watching close by. That blast from 747-sized Drogon's mouth would have incinerated everybody even remotely near. But as Varys' smoldering corpse lay there, it's clear nobody gave a wide berth.
Soldiers are ordered to shoot with the Scorpions by the command "Fire!" It does not make sense to use the word in a fictional world, where combustion weapons are not invented. The command for bow-type weapons would be "Loose!"