free speech and the rule of law).

Free speech and the rule of law were not absent in the Jacksonian democracy, but they did not meet contemporary standards. For instance, bureaucratic appointments were made to political favorites at every level, and they, in turn, used their administrative authority to support the Democratic Party. This system, called the "spoils system," helped cement the rise of party machines which undermined the equal application of law. Similarly, while there were no overt restrictions on free speech, those in power engaged in intense levels of coercion to limit it, including the suppression of attempts to mail abolitionist literature to Southern states.

Depends on who you ask from that time.  To come at this question from a different angle than the above posts, if you asked the Five Civilized Tribes sent on the Trail of Tears, they would argue Jackson was distinctly undemocratic.  The Supreme Court of the time, which ruled the Indian Removal Act was unconstitutional, was ignored altogether by Jackson, who removed the tribes anyway, so I would guess the Court would say there wasn't much democracy in Jacksonian Democracy.

While the phrase refers to Jackson's specific approach or philosophy of government as it compared and contrasted to earlier interpretations such as Jefferson's, the obvious hypocrisy of his actions, to me, makes the phrase a serious misnomer.

This answer only talks about Jackson himself.  I think that there is a distinction between Jackson the person and Jacksonian Democracy as an idea and as the distinguishing feature of an era.

Whether Jackson himself was power hungry is in some ways irrelevant.  Jacksonian Democracy as a whole was very democratic if you were a white man.  It was based on the idea that all white men should have the right to vote and the ability to participate in politics.

Of course, for a person of color or for a woman, this was not a democratic time.  These groups had very little in the way of rights.

Overall, then, regardless of Jackson's personal attributes, Jacksonian Democracy was very democratic for its time.  It was the era of universal white male suffrage and power for the "common man."  This was much more democratic even than the US had been prior to this era.

Andrew Jackson had a strong personality, a characteristic revealed by his nickname "Old Hickory", the toughest of America hardwoods. He brought this tough character to the American Presidency and stressed his individual authority which was often at odds with Congress. He used his right to vetoe Congress legislation more than all the previous Presidents put together. Jackson also opposed programs to make society more democratic such as educational reforms and freedom of religion. He also began the deportation of the Cheerokees along the Trail of Tears. As he was both the leader of Democratic Party and the President, Jackson concentrated an unprecedented power in a single person.

I think that much of this is dependent on your point of view.  On one hand, a case can be made the Jackson's presidency did increase democratic reforms and the idea of what democracy was.  There was an increase in suffrage, or voting rights.  Wealth and property ownership were not explicit preconditions needed to vote.  Instead, suffrage was extended to all white men.  One could even make the argument that the spoils system would help to increase to democratic initiatives in that the more one supported government and those in the position of power, the more representation they received in terms of recognition.  In the end, these elements brought more people into democratic government and their voices were included.  The flip side to this coin would be those who were not represented.  Women, Native Americans, as well as people of color were not automatically included in the equation of Jacksonian Democracy.  If one looked at their plights, then a case could not be made for democracy being expanded to more people in Jackson's Presidency.  I think that one needs to answer the question, balancing which side was more persuasive as to the issue of democratic reforms.

"Jacksonian Democracy" describes the general spirit of white egalitarianism and the actual expansion of the voting franchise that was associated with the politics of Andrew Jackson and the Democratic Party in the 1820s and 1830s. It coincided with territorial expansion in the United States, especially in the Old Southwest (Alabama, Mississippi) and Northwest (Kentucky, Missouri, Indiana, Illinois). Most of these new states, and a number of old ones, had looser voting requirements, allowing for white men with limited property to vote. Jackson deliberately campaigned by appealing to these new voters, and crafted his "Old Hickpry" image accordingly. Jacksonian Democrats evinced a strong distaste for eastern, especially northeastern elites. As president, many of his decisions (Indian Removal, the Bank of the United States veto) appealed to "the common man." Indian Removal underscored one of the fundamental contradictions within Jacksonian democracy. While white men had more political and economic opportunities than ever before, these opportunities came at the expense of Native Americans and African Americans, as many of these "common men" were moving into lands with the full intent of setting up small cotton plantations to be worked by slaves. 

Jacksonian democracy was the trend in which the United States became much more democratic.  It was a movement in American politics that brought about democracy for all white men.

In the years before the rise of Jacksonian democracy, the United States was much less democratic.  In many states, there were property requirements for voting.  Politics was seen more as a pursuit for the elites.  It was not something that the common people did.  In Jacksonian democracy, by contrast, politics came to be a mass participation process.  It no longer mattered if people were educated or not.  They could participate in politics and even be elected to important office.

This trend can be seen in the policy outputs of Jacksonian democracy as well.  The most obvious example of this was in the “Bank War.”  There, Jackson destroyed the Second Bank of the United States because he felt that it was a tool of the elite that was being used to harm the common people.  This sort of policy came out of the idea that politics was something that could be done by the common people and for the common people.