Yes, I saw that wikipedia link too. The thing is, it IS grammatically correct, what it is /not/ is the proper name of the party. That's partly why it's an epithet, to make fun of the Democrats' grammar.
As an analogy, I used to come across the same thing a lot in various MMOs I used to play. People would either name their character, or more noticeably their guild, something spelled wrong/grammatically incorrect. Something like an alliance guild in wow named "Should of played Horde".
Guild members would get mocked for it, especially the guild leader, but he couldn't change the name (not at first) and didn't want to go to the trouble of disbanding the guild and re-chartering it with the correct grammar. So "Should of..." was the proper name of the guild, but it was grammatically incorrect.
Another reason it ("Democratic party") was made fun of is because "democratic" is an adjective, a descriptor, and as far as I know, the Republican party actually behaves in a little more democratic manner than the Democrat party. They just do it more slowly, more conservatively.