I think the Toast error explains the behavior on your Mac. Errors are errors. It happens.
For dedicated DVD players, you need to be careful. Since they don't operate at high speed like PC DVD drives, any error will create skipping. On your Mac, if the drive has trouble reading a sector, it has time to try a few times before the problem creates skipping. On a dedicated DVD player, it has to work perfectly.
For this reason, it's generally recommended to burn your DVDs at the
lowest possible speed. This creates less variation on the surface, making it easier for drives to read it properly. The same applies to CDs, too (although I don't think that's really a problem with modern players).
Also, are you sure your DVD player can play DVD-R discs? I assume any player that can play them at all should be able to play them properly given a good disc, but you should look up your player at
http://www.videohelp.com to be sure. Keep in mind that there are
four major writable DVD formats (more if you count the dual-layer variants), and they all have different drive compatibility.