The dog that didn't bark
This approach comes from a Sherlock Holmes story! Basically it comes down to "if situation (a) happened, then why did not situation (b) happen? Or - maybe it did, but the police case did allow for it. It is a matter of applying common sense to a scenario using experience of the real world and how people react to it - rather than accepting the falsities that can creep into a manipulation of the facts that can happen when someone is trying to prove a case against someone.
Sometimes the prosecution - and in particular the police - tend to think "Well we know our suspect is guilty because of (a) - so, although (b) seems unlikely, it must be so."
Our response to this is "Well (b) seems to fit in with the way the world actually works, so perhaps there is something wrong with (a)."
The basis of this thinking is that life tends to happen in much the same way throughout the world. In the Sherlock Holmes story, a guard dog does not bark when a crime is committed - how could that be - it is trained to bark at such times. Was it drugged? - no. Was it clubbed senseless? - no . Who on earth could get past a good guard dog without it barking? Well - clearly its owner.
So, perhaps in a case where the police claim the suspect said something incriminating to them whilst in the car going to the police station, yet neither officer noted the remark in his notebook - even though other remarks in the car are noted. How could that be?
Perhaps in another case the police produce a photograph to show that the suspect had a particular line of sight which is significant. The street is empty of cars. Are most streets like that? And who can move cars from streets most easily? A visit to the scene is merited - to witness the normal view that someone might have.
Or - the victim is found in a field. She was apparently attacked in the morning. But it rained in the morning and she was wearing high heeled shoes. Would she really walk over a soggy field in them - and where are the footprints?
A variation - the victim buys some new shoes. A day later she is murdered. The murderer is said to have followed her through some woods, over a stream where there are stepping stones. He finally caught up with her by an old disused railway line. Do girls normally trudge through the mud and over stepping stones in new shoes? Could she perhaps not have reached the scene of crime by walking along the disused railway line?
A girls gets off a bus on her way home. She has been shopping and bought some paint for decorating her home. Several people see her put her umbrella up - because it is raining. She is attacked on the pavement not far from her home - and discovered because someone sees the paint can, knocked over, with the paint in spots on the pavement- leading into a nearby garden. She has clearly tried to defend herself with her umbrella, because some of the spines are bent. A suspect is quickly found. He has spots of paint on his shoes - the same colour as the victim's paint. Pretty conclusive - except look at the photos of the paint on the pavement. It must be water-based, because it has been affected by the rain - the spots have soft edges. The suspect's shoes have spots with hard edges - unaffected by the rain - how could this be?
Again - incriminating fibres are found on the knees of a suspects jeans. Yet none were found on his trainers which he was wearing at the time. How can this be?
The basic rule here is - apply the normalities of the real world to the artificial world of the police scenario.