Revealing mistake: The shout where the paedophile's car gets petrol-bombed was done using CGI. The flames are not consistent between shots and there is no smoke whatsoever.
Continuity mistake: When Billy and Sicknote go upstairs after their encounter with Pitbull, they go upstairs to change into uniform. The camera follows them upstairs. The appliance bay has no other firefighters present. When the camera pans back down, a full roll-call is taking place in the appliance bay, including Billy and Sicknote who just went upstairs to change few seconds earlier. This was probably done intentionally but it sure does look ridiculous.
Factual error: In series 13, when phone numbers are referred to, they usually start 0808 (even mobile numbers). UK phone numbers starting with those numbers are freephone numbers and wouldn't be used for private use, or even for mobiles (which all start with 07).
Revealing mistake: During the flat fire, the girl tosses her baby to ADO Coleman. Just before he catches it, you can see that the falling baby is a doll.