@6: If the question had asked whether or not this evidence would have resulted in a conviction, I'd have said 'yes'. It's logical to say it is highly likely she committed the offense, but it's not a certainty. I gave the answer 'invalid' because it was asking for a logical proof, rather than being beyond reasonable doubt.
The water one is debatable, indeed. Their objections are that it only holds true if water is defined as it is in the first premise (!), and that it only holds true if what we're examining is actually water, which we're told it will be. The conclusion also states that we can make a prediction about future examination of water, not that we can make a prescriptive statement; predictions can be valid and still fail.
The headline is a bit misleading, saying that needle-free injections have been invented. The comment under the video says "a Japanese inventor says he's gone even further to cut costs and improve efficiency.", which means that this guy's design is a development, rather than an invention.