Some examples off the top of my head:

Rodney Brooks and others published many papers in the 1980s on reactive robotics. (Yes, reactive robotics are useful for some tasks; but the claims being made around 1990 were that non-symbolic, non-representational AI was better than representational AI at just about everything and could now replace it.) Psychologists and linguists could immediately see that the reactive behavior literature was chock-full of all the same mistakes that were pointed out with behavioral psychology in the decade after 1956 (see eg. Noam Chomsky's article on Skinner's Verbal Behavior).

To be fair, I'll give an example involving Chomsky on the receiving end: Chomsky prominently and repeatedly claims that children are not exposed to enough language to get enough information to learn a grammar. This claim is the basis of an entire school of linguistic thought that says there must be a universal human grammar built into the human brain at birth. It is trivial to demonstrate that it is wrong, by taking a large grammar, such as one used by any NLP program (and, yes, they can handle most of the grammar of a 6-year-old), and computing the amount of information needed to specify that grammar; and also computing the amount of information present in, say, a book. Even before you adjust your estimate of the information needed to specify a grammar by dividing by the number of adequate, nearly-equivalent grammars (which reduces the information needed by orders of magnitude), you find you only need a few books-worth of information. But linguists don't know information theory very well.

Chomsky also claims that, based on the number of words children learn per day, they must be able to learn a word on a single exposure to it. This assumes that a child can work on only one word at a time, and not remember anything about any other words it hears until it learns that word. As far as I know, no linguist has yet noticed this assumption.

In the field of sciencology?, or whatever you call the people who try to scientify science (eg., "We must make science more efficient, and only spend money discovering those things that can be successfully utilized"), there was an influential paper in 1969 on Project Hindsight, which studied the major discoveries contributing to a large number of US weapons systems, and asked whether each discovery was done via basic research (often at a university), or by a DoD-directed applied R+D program specific to that weapon system. They found that most of the contributions, numerically, came from applied engineering specific to that weapon system. They concluded that basic research is basically a waste of money and should not have its funding increased anymore. Congress has followed their advice since then. They ignored 2 factors: 1) According to their own statistics, universities accounted for 12% of the discoveries, but only 1% of the cost. This by itself shows basic research to be more cost-effective than applied research. 2) They did not factor in the fact that the results of each basic research project were applied to many different engineering projects; but the results of each applied project were often applied only to one project.

NASA has had some projects to try to notify ETs of our presence on Earth. AFAIK they're still doing it? They should have asked transhumanists what the expected value of being contacted by ET is.