According to Mill, what are the limits that can be placed on freedom of speech?
In Mill's thinking, it is essentially never acceptable to place any limits on people's freedom to say what they want. As Mill says (quote in the stanford.edu link),
the only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others.
From this, we can see what Mill would say about limitations on the freedom of speech. He would say that speech may only be limited if the speech would harm other people.
This is, of course, something of a vague standard. We have to ask what constitutes a "harm." This is very difficult because we will have to determine what sorts of harm matter and how much they are outweighed (if at all) by the good that comes to society from the freedom of speech.
In general, though, Mill says that very few limits may be placed on the freedom of speech.