Thank you all!
@tautech: Yes, my SDG has behaved like this since I received it -- which was only 3 weeks ago. I just checked, and it does have the latest firmware installed, V2.01.01.23R8.
I just played with the buttons some more, and realized that it's really mainly one of them which is giving me problems: The 3rd softkey from the left, which happens to be the offset/low level selector when setting waveform parameters. All other buttons hardly ever bounce, the 3rd one does it all the time.
Obviously the unit is still under warranty, and I could contact Batronix and ask for a replacement. They have a good reputation for customer service. But I am tempted to try and avoid the hassle and delay of shipping the unit, and have a look myself first. With only one button affected, it seems likely that there is simply some piece of debris in the wrong spot...
I don't want to risk my warranty of course. How invasive is the procedure to get to the contacts? The service manual suggests that you can't open the front from the outside, but have to open the unit, remove the front panel unit, and then get to the keypad from the back -- is that the best (only?) way?
Update: Some strategic finger-snapping against the affected button seems to have improved things a lot! Maybe indeed a piece of debris, which I managed to dislodge?