Last week I signed a contract for a gym membership with the wrong location. I'm not really aware of how contract signing is handled in other countries, but here in Germany it always is a part of it. Out of sheer habit I wrote the postcode and name of my hometown instead of the location where I signed the contract. The other party, and me, did not notice at that point. I just noticed while filing it at home.
Is such a contract correct/legal? Should I get a new contract and/or tell the other party about my mistake? The contract itself is totally fine, it's not like I gave a wrong address or something. Just the location of signition is wrong.