Have the core CBT "Thinking Errors" been found to NOT be effective in evidence-based clinical practice? This is his chart of the ten "thinking errors." It's taken from The Feeling Good Handbook.


  Table 3–1. Definitions of Cognitive Distortions
  
  ALL-OR-NOTHING THINKING: You see things in black-and-white categories. If your performance falls short of perfect, you see
  yourself as a total failure.
  
  OVERGENERALIZATION: You see a single negative event as a never-ending pattern of defeat.
  
  MENTAL FILTER: You pick out a single negative detail and dwell on it exclusively so that your vision of all reality becomes darkened,
  like the drop of ink that colors the entire beaker of water.
  
  DISQUALIFYING THE POSITIVE: You reject positive experiences by insisting they “don’t count” for some reason or other. In this way you
  can maintain a negative belief that is contradicted by your everyday
  experiences.
  
  JUMPING TO CONCLUSIONS: You make a negative interpretation even though there are no definite facts that convincingly support your
  conclusion. 
  
  a. Mind reading. You arbitrarily conclude that someone is
  reacting negatively to you, and you don’t bother to check this out.
  
  b. The Fortune Teller Error. You anticipate that things will
  turn out badly, and you feel convinced that your prediction is an
  already-established fact.
  
  MAGNIFICATION (CATASTROPHIZING) OR MINIMIZATION: You exaggerate the importance of things (such as your goof-up or someone else’s
  achievement), or you inappropriately shrink things until they appear
  tiny (your own desirable qualities or the other fellow’s
  imperfections). This is also called the “binocular trick.”
  
  EMOTIONAL REASONING: You assume that your negative emotions necessarily reflect the way things really are: “I feel it, therefore
  it must be true.”
  
  SHOULD STATEMENTS: You try to motivate yourself with shoulds and shouldn’ts, as if you had to be whipped and punished before you could
  be expected to do anything. “Musts” and “oughts” are also offenders.
  The emotional consequence is guilt. When you direct should statements
  toward others, you feel anger, frustration, and resentment.
  
  LABELING AND MISLABELING: This is an extreme form of overgeneralization. Instead of describing your error, you attach a
  negative label to yourself: “I’m a loser.” When someone else’s
  behavior rubs you the wrong way, you attach a negative label to him:
  “He’s a goddam louse.” Mislabeling involves describing an event with
  language that is highly colored and emotionally loaded.
  
  PERSONALIZATION: You see yourself as me cause of some negative external event which in fact you were not primarily responsible for.


Has using these errors as a therapeutic tool been found to be effective in clinical psychotherapy?
I think you should change the question a little bit to "What should be done to the Thinking Errors?" or "Just identifying and evaluating Thinking Errors might not be effective?". Yes, they may not be effective. Please be careful that all mental problems need to be treated by professional therapist and a very important part of their expertise involves the diagnosis. There are many anxiety or depressive disorders that they manifest similar "Thinking Errors" kind of thinking, but they have different underlying causes and should be treated differently. It's not to say that strategies like those described in The Feeling Good Handbook don't work, rather they work when things are simple. If you feel that things are more complicated you should surely seek some professional advice.

To illustrate this point to you by an example I would like to mention Obsessive Compulsive Disorder (or OCD). In OCD, there are some problems in cognitive system that makes the person being constantly paralyzed by lots of Intrusive Thoughts. The content of these thoughts may be similar to "Thinking Errors" or could be corrected by similar strategies, but focusing on them and trying to correct them make them stronger, more sailient, and more frequent. People with this disorder then feel that they are compulsively correcting their erroneous thoughts, but it seems they can never get rid of them. For this disorder, another treatment strategy has been offered called Exposure and Response Prevention (EX/RP). In this kind of treatment people are encouraged to face their intrusive thoughts, but don't respond to them.To try to accept their presence and at the same time not to let them to make them do anything, or not do anything. There is abundant evidence that EX/RP is effective for OCD.

And there are also other disorders with their idiosyncrasy. I'm not sure what kind of problem you're describing, but if you want to use self-help method (with all it's pro and cons) you could take a look at diagnostic features of OCD.