The research indicates that the best approach is to direct attention to wanted behavior and away from any harmless unwanted behavior that can be ignored.
This is actually the strategy my parents applied a lot (I observed that on my younger siblings). On problematic issues distract from it by supplying something entirely else and focussing attention on that. But it made me feel uneasy because it didn't (seem to) address the real issue. It looked like an easy way out. It did work but it also cost quite some time each time.
The strategy of signaling that you notice, smiling at, gamifying, in response to unwanted behavior is grossly counterproductive.
This is valuable advice. Thank you.
But the point still stands: If the children notice that you intentionally condoned than you relativize your consequence. You can only do this if a) you accept this lenience or b) are sure that the (small) child will not notice. And if the act is indeed harmless.
On the other hand one can nonetheless signal in a mild form that you noticed in really harmless cases.
I will not gamify anymore though.
(how do I make those bars on the right indicating what I am replying to?)
"But it made me feel uneasy because it didn't (seem to) address the real issue. It looked like an easy way out. It did work but it also cost quite some time each time."
You can always address the real issue at some other time. The key is merely short-term timing, you don't want to react immediately in a way that reinforces the unwanted behavior with attention. Later, when the kid is not engaging in unwanted behavior your can address the real issue for hours on end if you w...
Followup to: Strategic ignorance and plausible deniability
My in-law always says: "For children it is easier be forgiven then to get permission."
EDIT: This post is superseeded by my Book Review: Kazdin's The Everyday Parenting Toolkit I recommend reading only that. The remaining insight of this post is: Children expend more brain power on their parents than the parents on them.
I can say from experience: That is risky.
Children (esp. small ones) expend significantly more brain power on their parents than the parents on their children (your mileage may vary). I can assure you that they will notice these cases - at least some - and take that into account one way or the other.
If the children notice this they may assume that you either condone, accept, bear or ignore it. None of these has positive effects.
Possible alternative strategies:
I am influenced by The Adlerian School. Of relevance here is Striving for significance.
The testing of limits and the resulting interaction with the parent give the child a feeling of significance if the parent acknoledges the act of the child even if he doesn't agree with it. On the other hand ignoring the act of the child is negative feedback about significance.
EDIT: The asymmetry between parents and children with respect to the effectiveness of deniability can be generalized to any situation where one actor has significantly less overall information about the situation than another actor and thus might not be able to reliably estimate whether deniability is possible.
ADDED: tadamsmar pointed out that ignoring is scientifically known to be effective and the advice or rather personal expierence I have related in this post may be contraproductive (at least if applied in isolation).