And, yet, you've spent lots and lots of energy and you can't find the problem yourself. And what if there is something there? There are many famous cases of experiments that weren't confirmed by theory until well after the fact; theorists often don't bother to think about a particular corner of the unthinkable until an experiment calls attention to it. So you've just got to publish your data, but also be prepared to laugh it off when the mistake gets identified, or the data proves irreproducible. And then to spend the rest of your career laughing it off, because this spurious result may be the most famous thing you ever publish.
You've got to have a good sense of humor to survive as an experimentalist.
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[1] I wish I remembered which teacher said this.
From Gary Taubes' (the author) website: Bad Science: The Short Life and Weird Times of Cold Fusion is book of science history by Gary Taubes about the early years (1989–1991) of the cold fusion controversy. It is not a scholarly work, but a popular retelling of the events, based on interviews with over 260 people. The book presents a timeline of the events, making the case that the cold fusion field has many examples of poorly-performed science. The actions of Martin Fleischmann, Stanley Pons, and Steven E. Jones, the scientists who made the dramatic first claims of fusion, are described in rich detail. The book then shows the worldwide reaction and later disrepute of the cold fusion field, with Taubes placing himself in the side of "good science". Taubes says at the end that cold fusion had only demonstrated that research can continue even if the phenomena doesn't actually exist, as long as there is funding available. Taubes had previously written an article for Science in which he insinuates that the cold fusion work of A&M University was fraudulent.
The speed of neutrinos is less interesting, because I don't get anything out of it right now. A "huh" and some new physics textbooks and all that, at best.
(I'm personally excited, but that's because I am more excited by unlocking the secrets of the universe than by being able to drive an SUV for free. Because I already have a vehicle whose energy source is practically free.)