Welcome! Wow, Switzerland! Even here in the States, the Reatta is becoming more rare by the day. I can't imagine there's more than a couple in your country IF THAT.
I agree with those above on checking the alternator. Can you or your mechanic test for AC voltage at the battery while under a heavy load? Even a tiny ripple of AC voltage can cause havoc on digital displays.
You also mentioned that your battery may be weak. Keep in mind: a car NEEDS a strong battery not just to start, but to provide a buffer between the alternator and the vehicles electrical system. For example, the Reatta comes with a 105A alternator. However, that 105A is only produced at cruise RPM's. At idle, it's output could be as little as half depending on age and condition. 50A is EASILY spoken for by the full complement of exterior lights on a Reatta. Anything more than that, and you're begging for issues.
Replace the battery, test for AC voltage, and report back.