Free speech jurisprudence is rich and broad, but two First Amendment concepts are particularly important to filmmakers: defamation and journalistic privilege.
Defamation is a false, publicly-made statement about a particular person or company that diminishes that person's or company's standing in the community. Or, put another way, it's an untrue statement that harms the target's reputation. Defamation comes in two flavors: slander and libel. Slander is spoken defamation. Libel is written defamation.
A statement could be defamatory because of its literal meaning. “Director X doesn't pay his crew or his taxes." But something could be defamatory by implication. “Having seen how he manages his crew, I wouldn't work with director X” doesn't convey any specific facts, but it suggests unprofessional and possibly unethical behavior.
The statement must be about a specific and identifiable person. A general comment about lawyers, for instance, doesn't refer to anyone specific, or even to a specific enough group, so no claim of defamation could be brought, no matter how harsh the comment.
Publication means saying it to just one other person. An email, a phone call, a text are enough. If something is in a film, especially one that's been distributed, it will be presumed published.
As a quick glance at Twitter reveals, though, not all negative statements are defamatory. Some types of speech, even though critical of others, are nevertheless protected.
1. True statements are generally--though not always--protected, since truth is generally--thought not always--seen as a defense.
2. Opinions are protected, so long as it's clear that they're opinions, and as long as they don't suggest that the speaker is basing that opinion on undisclosed facts that, if false and alleged, would be defamatory.
Journalistic Privilege/Reporter's Privilege
In some cases, journalists may have a First Amendment basis for refusing to disclose information or materials requested pursuant to a subpeona. A filmmaker could refuse to comply with a subpoena that, for example, demands footage from a project or the disclosure of a source's identity.
The analysis is fact specific and has to take into account jurisdictional variation as well as the type of proceeding involved (grand jury, criminal trial, or civil trial). Generally, however, in order to assert this privilege the filmmaker has to show that the project is--and, importantly, has been--from its inception a form of independent journalism. So, if the work is commissioned by someone (e.g., a company) to make a commercial, the privilege likely will not be available, since it's neither independent nor journalism. But if the filmmaker can show that the project is a type of investigatory journalism and has been undertaken with a view to publication, the privilege may well be an option.