Again, no expert but here's a linkie:
Appears to me that you are starting with this "Sonata" format and your standalone DVD player is failing to erase all the files.
The introduction of the DVD player to the equation creates some questions. I had assumed all your "manipulation" of the DVD disk(s) was being done on the computer and only with Nero.
Can I ask why you are erasing the DVDs on the Player, when Nero will do that ? It seems to be an "oddball" factor that might be the cause of the problem.
Also, did you check to make sure that you are not finalizing these disks during burn ?
Are you only burning with Nero, or are you recording from the Player as well ?
In my limited experience with DVD burning, I have never seen any other files besides the Video and Audio ._TS files (and it's my understanding that the Audio folder is always empty and isn't even needed to play the video).
Perhaps this RW disk had the Sonata format, was incompletely "erased" and another format was burned to it, thereby causing some sort of conflict because there are two video formats on one disk ?
But then you didn't say you had trouble playing, it was re-recording that was the problem.
Is all of this centered on one particular disk, or do you experience it on more than just one disk ?
If more, does it happen over different brands of disks ? The DVD gurus constantly talk about poor quality media and how important it is to avoid it. I would assume this is particularly true for RW media.
What brand(s) are you using ?