Mr. Walters's answer is quite comprehensive!
There are two other areas that imply limits on freedom of speech. Pirkei Avot 1:17 gives a general admonition towards "excessive" speech:
Shimon, his son, says, "All my days I grew up among the Sages, and I
did not find anything good for the body except silence. And the
exposition [of Torah] is not what is essential, but the action. And
whoever increases words brings sin."
The last sentence is hard to understand within the context of the rest of the advice. The first sentence seems to advise not to talk at all. The second implies do more than study. And the third sentence implies if you talk "too much", you lead to sin.
Barternura explains the last two concepts:
If you don't practice what you teach, you would have been better off being silent. That seems to be one example of "excessive speech".
The second explanation (from Sefaria):
"and anyone who increases words, brings sin": As such have we found
with Chava, who increased words and said, “God said, 'Do not eat from
it and do not touch it,'” and added touching, about which she was not
forbidden. And the snake pushed her until she touched it and said to
her, “In the same way as there is no death from touching, so [too] is
there no death from eating.” And from this, she came to sin, as she
ate from the fruit. This is what Shlomo said (Proverbs 30:6), “Do not
add to His words, lest He reprove you and you be found a liar."
Devarim 23:24 says - "Watch what comes out from your lips".
While this expression is related to vows, namely that you must fulfill and commit to your (verbal) vows, (similar to the above that suggests that you should do what you teach), you could probably apply this expression to general behavior. I.e. - speak nicely. If you promise to do something (even if not a "vow") you should keep your word.
Regarding vows, one or two verses prior to the one I mentioned says, "If you cease to vow, there will be no sin". Again, this is in line with what Pirkei Avot says, "excessive speech leads to sin", as in the case of a vow that you can't fulfill!