Words of wisdom are so often helpful that many of them have solidified into easily remembered capsules. We do tend to over-generalize them, though, and when we do, trouble follows. Here are a few of the more dangerous ones.
Words of wisdom usually are short, pithy sentences so sensible that we accept them unquestioningly. An example from George Santayana: "Those who cannot remember the past are condemned to repeat it."  

But unquestioning acceptance can be a serious mistake.
Here are some common ideas worth at least a pause for thought.  

It took a long time for this crisis to develop, and it will take a long time to resolve it.  

     This statement’s symmetry is appealing, and it’s often true, but it lacks logic. The processes that led to crisis often differ from those that resolve it.

     Crisis resolution happens on time scales compatible with the means employed, rather than the time scales of the forces that created the crisis. The two time scales rarely bear any relation to one another.

Yes, that approach did work on that problem. But this problem is different, so we have to use a different approach.      

     There isn’t much solid reasoning here. For instance, if we must transport someone to a hospital for treatment following a fall, the means of transportation can be the same for a broken left collarbone as for a broken right collarbone. Two different problems, but one approach works for both.

     Similar solutions can sometimes work on dramatically different problems. It can be foolhardy to discard candidate solutions simply because they worked on problems markedly different from the problem at hand.

We'll get out of this mess faster if we first understand how we got into it.      

     If the effectiveness of a candidate solution depends on the genesis of the mess, this idea might help. But in many difficult problems, the forces that created a problem become irrelevant once the problem has taken hold. Those forces can differ from the forces that maintain the problem, and from the forces that propagate it.

     Before investing in costly efforts to determine underlying causes, understand how the information you seek will actually be useful.

Pick the low-hanging fruit first  

     In wide use throughout the English-speaking business community, this metaphorical reference to fruit picking suggests that low-hanging fruit is appealing because it’s so easily picked. But this metaphor, like many others, is misleading. Although low-hanging fruit is more easily picked, it’s often inferior in quality, because it tends to have been picked over fairly thoroughly by other pickers. It often lacks sugar content and ripens later than “high-hanging” fruit because it receives much less sunlight.

     Fruit that’s a little more difficult to pick might actually yield a higher return on effort expended. So it is with real-world problems.

Words of wisdom might well apply to these situations. Beyond those situations, knowing when to apply another's wisdom, and when not to, requires wisdom of your own.