Producing DVDs that play everywhere
You can't make a DVD that plays on all players.

Unfortunately for your distribution, @Flimzy was correct with his explanation of most compatibility problems, and only left out the PAL/NTSC issue, which simply put, means that even if you don't have region encodings, or if you get them correct, then many (if not most) DVD players won't play the opposite type.

The best you may be able to do, is focus on media types.  Replicated (pressed) DVDs (not burned) are going to play back on the most devices without trouble.  After replicated disks, in a distant second place for compatibility, comes re-writable disks.  Least likely to play are single-write disks.  But, when you use writable and rewritable media, your disk is either more or less likely to play on any single DVD player, depending on the make and model.