CID would not be called to investigate the crypt break-in at the churchyard unless the PC who first attended the job had established that a more serious crime had been committed. Similarly, a detective sergeant subsequently attending would never call out a detective inspector without also first establishing a serious offense. When Frost arrives, all anyone knows is that someone has broken into the crypt and rung the bell, which could be easily handled by the PC and most certainly by DS Gilmore if he'd still been asked to attend. The only reason Frost would have been called is if they'd found Paula Bartlett's body inside first. Although Frost and Gilmore were supposed to already be there keeping it under surveillance (and the uniformed branch would have known this), the scene plays out as if those plans were never in place and the dialog between the officers makes it sound like a routine call-out. The novel (Night Frost) made sense of this scene by having the uniformed branch call Frost/Gilmore asking where they were upon responding to the churchwarden's report, and Frost pretending that they were at the other end and quickly racing back to meet the PC at the crypt; for some reason, the episode did not follow this, resulting in the error.
A common goof in any number of UK police dramas - Frost talks to Bell in his kitchen where he admits everything. There was no indication of his being cautioned and there are no witnesses present. Very likely this confession would be dismissed as having no real legal standing. This interview would take place in a police interview room and be recorded as per PACE (1984).
The dead girl's eyelids can be seen to flinch.
Frost fits up Bell by pretending to find a charm (from the dead girl's charm bracelet) in the back of his car. But Bell and the girl's stepfather had already confirmed she took lifts in his car. Thus the charm isn't proof of anything (never mind being planted).