What are the problems with merging DB dumps? A strategy I've used with ExpressionEngine for managing the CMS in different environments is to use Git to merge the DBs of my dev and live environments when I need to deploy something new to live. This is working really well for me, my users are creating content but I can code without fear at the same time.

I see comments here and here that make it seem like the same is not true for Drupal 6. Is this just a question of the size of the database (which I think I could cater for by ignoring certain tables), or are there other concerns?
If you use Git to version DB dumps and merge dumps from dev. and live, you can also do that with Drupal. But the Drupal DB schema is dynamic, new modules add new tables and some configuration (mainly CCK) changes can add or remove columns or rename tables. Because of this, handling (configuration) changes with DB dumps merge is hard and error prone. That's why alternative methods like Features-driven workflow are recommended to manage (configuration) changes management between multiple environments.

See also The Development -> Staging -> Production Workflow Problem in Drupal and the Code driven development: using Features effectively in Drupal 6 and 7 presentations.