>> This seems backwards to me. German law is supposed to be consistent with the constitution, so is, essentially, a logically consistent system. If you can prove a logical inconsistency with basic law, then you can win a case on that basis. That makes it more or less understandable, because the entire corpus of law follows logically from a short, comprehensible kernel.
This is typically the case in common law systems with a written constitution as well (the US, Australia, India, etc). Laws not consistent with the constitution generally get stuck down as invalid to the extent of any inconsistency.
In practice, of course, most day-to-day cases do not engage with constitutional principles in either system. If you're facing a criminal charge of larceny, and you're searching the Constitution / Basic Law for your defence, I might diplomatically call your approach... bold.
>> Secondly, precedent is a pretty good guideline to what will actually happen.
>> Making precedent binding seems a bit crazy, to be honest, because if the precedent contains mistakes (which it inevitably does), then those mistakes become binding also, right? So logical inconsistency and contradiction is inevitably part of the common law system?
This is a great question! Precedents can and are overturned in several ways in common law systems. A higher court can overturn a lower precedent, and generally also its own previous precedents. A lower court is more restricted, but perhaps the most common way to avoid a precedent is to "distinguish" it - this means to basically claim that the two cases are not alike, and so the precedent ought not apply. (Very loosely speaking, precedent is only binding on alike cases - this is the basic theory of precedent, that the case has already, in fact, been decided before. The Latin term you often hear for this is stare decisis.) This is tricky, and higher courts will rap lower courts on the knuckles if they're not obeying precedent that binds them without good cause.
But more broadly it's important to remember that precedent ("common law") is subordinate to written law ("statute law"). So if the legislature passes a law, and the judiciary interprets it in a way that the legislature doesn't like, the legislature is entirely free to amend that law to correct the court's understanding, which renders the precedent moot. The one exception is constitutional law, which might be more complicated to amend (referenda may be required), so courts have to tread carefully.
(None of the above is legal advice.)