Okay, seems that the continuity errors disturb Kodi and even VLC playback.
I replaced the LNB and all cables, adjusted the dish and my sat finder (WS-6933) shows now >15dB signal rate (compared to <14dB with the old LNB). The result was quite the same - 100% signal quality but, especially on some H/V low-band transponders, a bunch of continuity errors.
The only things I didn't replace yet is the dish itself (85cm), the multiswitch and the Sat-IP receiver.
As I don't expect the dish causing the issue, I measured the signal rate at the multiswitch output.
The signal fell from ~15.8dB at the input to ~11.0dB at the output. I tried to skip the multiswitch (as the new LNB has a multiswitch) and the errors disappeared.
Saying that - the root cause might be the almost 10 year old multiswitch. I'll replace it soon with a better one and keep you informed if the issue has been solved!