Not really this is one of those rules that makes people think they can win court cases that they can't really win. The idea that if you catch the police in a small error you can get off in a criminal case. You have to catch the police in a big error that they based the case off, or a serious breach of your rights. This will hardly ever work.
There are others :
1) If I follow the law I won't lose a case. Cute. Try being unreasonable to a judge and see how that works (A popular one : tell the judge that because a car accident happened on your own property, you got to set traffic law governing that accident. Technically correct. Try it)
2) If they don't have proof I can't be convicted. (and sometimes : video is not proof). False (well the video thing is true). The big mistake here is civil versus criminal cases. If it's not the government suing you, or "technically" not the government, e.g. mall security, then proof is not required, and video is perfectly admissible. Even if you are not recognizable on the video, but there's good reason to think it's you (e.g. a credit card record). Second, witness statements from people watching video can be accepted sometimes.
3) If the opposing party makes one tiny mistake I can get off scott-free. False. The justice system's job is to make the smallest possible change to the arrangement that makes it legal. If you sign a contract "I will kill my firstborn and pay $200" (extreme, ridiculous example), obviously you do not have to kill anyone, you will however, be on the hook for the payment. Interesting cases result from the use of "or" instead of "and".
This goes for government integrity too. Suppose Ulbright's lawyers get this one. The next thing that happens is the judge telling the prosecutor to go home, have a good night sleep, start the case from scratch and try again (in the same court case). If he succeeds, that's fine (of course he might not be able to).
4) With a lawyer I can tie up any case for any amount of time. No you can't. Ridiculously complex contract law cases, yeah sure (even then best take a good lawyer). Not paying your car repair bill, no.
5) They can't get to me if I move/hide/other state/other country/... Might be true. Not true for any place worth living. So good luck with that.
These things should be taught, with a few example cases illustrating what can happen. It would lessen the load on the justice system by 50%.