1 There's no smoke without fire.This suggests that there is no such thing as a completely unfounded rumour or accusation. While most people would reject that suggestion if put in those terms, this well-known and frequently used saying still has the power to persuade. It shouldn't. Too often, when an accusation is made, we assume for no good reason that "there must be something in it". This readiness to believe something negative without evidence is probably an over-reaction to not wanting to be naive.
2 If it ain't broke, don't fix it.Trivially true about machinery, perhaps, but few aspects of human life are simple enough to be described as either broken or not broken. Most may not be perfect but are probably not in need of a complete overhaul either; they need improvement. The "If it ain't broke" approach is just an excuse for apathy. We don't need to think in terms of "fixing" things, but we can aim to make them better. Conservatives love this saying because it has homespun charm, unlike its more honest translation: "Let's not change anything unless we really have to."
3 A leopard can't change its spots.Or to put it another way, "Once a criminal (adulterer, liar, etc) , always a criminal (adulterer, liar, etc)". But why exclude the possibility of reform or rehabilitation? An equally valid saying which expresses the opposite view might be "a snake sheds its skin", implying that radical change is part of normal development. Unfortunately, the ultra-conservative and pessimistic saying is the one which actually entered the language.
4 Old enough to do the crime, old enough to do the time.People have a tendency to believe without question anything that rhymes. This no doubt has its roots in childhood and should really play no role in the adult psyche, but it's evidently hard to shake off. There are many examples, but the one about doing a crime and doing time is a favourite among politicians wishing to sound strong on law and order. The rhyme functions are a kind of surrogate logic and seduces us into thinking an argument has been clinched. In reality, it's just a bald assertion that if children commit crimes we should lock them up - although it doesn't sound so good put in those terms.
5 An Englishman's home is his castle.More often than not, this is trotted out as an excuse to shoot intruders. Harking back to an era when law enforcement was a private affair, it implies that the right to defend your own property is sacrosanct and the state should basically butt out. But times have changed. While your home should certainly be a haven of safety and security, calling it a castle does not give you licence to pour boiling oil on would-be trespassers.