First of all, freelance editors and writers are often sent boilerplate contracts that include clauses requiring liability insurance--which might make sense if you are rebuilding a wing of a building, but rarely make sense for a writer and certainly not for an editor. My advice (gained from others' experiences): Cross out that clause and tell the client that it isn't relevant because (if true) you dont have employees, work onsite, travel on behalf of the client, see clients in your home office, operate heavy equipment, endanger the general welfare, and so forth. (Hat tip to Ruth E. Thaler-Carter for the wording.) If you raise an objection based on common sense, the client is likely to tell you just to strike the clause. If they don't and the fee is low, it probably won't make financial sense to sign the contract, or at least I would not do so. See also what Will MacPheat reports, in the Comments section.
Meanwhile, here's the best round up of information I have come up with for if you DO find yourself in a situation where you need to buy the insurance. Media perils liability insurance (or publishers liability insurance) may provide you with protection for such traditional claims as copyright infringement; libel; defamation, plagiarism; invasion or privacy or publicity or infringement of privacy or publicity rights; misappropriation of trademark, title, or slogan; defamation; misappropriation of property rights; personal injury; contextual errors and omissions.
What is covered depends on your policy so if there is any chance of your being vulnerable to a lawsuit, study your threats and options. You are protecting mainly against lawsuits, and I am no lawyer, so I report only on what I have learned over the years. I cannot recommend a particular insurance firm or broker, but just finding one is not easy so I list a few others have recommended. If you don't need the basics explained, scroll down to the section on Where to find liability insurance for authors and indie publishers
Be careful what you agree to in publishing contract
How to Deal with Warranty and Indemnification Clauses (Writers & Editors site)
Contract terms (especially but not only in book publishing) '
Media perils and publishers liability insurance, broadly
I am a freelance journalist. Do I need to buy liability insurance? (Annalyn Kurtz, Columbia Journalism Review, 11-13-17) "Do not make the mistake of buying a basic general liability policy online, without considering some intricacies of media law." Do read this important article.
Liability Insurance Nyet (Rich Adin, Business of Editing, An American Editor, 5-22-13). When a client insists that a freelance editor have errors and omissions insurance, what does the editor do? Explain why it makes no sense for editors.
Get Covered: Media Insurance for Writers (Tara Lynne Groth, Women on Writing, Nov. 2010)
Media perils insurance protects against lawsuits over libel, copyright infringement (Jennie Phipps, What Freelance Success Says, 5-19-11)
WriteInsure, through Axis Pro/Argo Insurance Group (media and entertainment liability coverage, professional and miscellaneous errors and omissions, and cyberspace liability). Leading underwriter of media liability insurance. Available through Authors Guild and ASJA, among other organizations. Axis Pro offers four levels of coverage through WriteInsure, ranging from $100,000 per claim (with an aggregate payment limit of $300,000) to $1,000,000 per claim (with an aggregate payment limit of $1,000,000). The program covers legal expenses incurred in defending a claim and any monetary damages or settlements you may be required to pay. The "self-insured retention" (similar to a deductible) ranges from $2,500 to $5,000, depending on the amount of coverage you purchase. See WriteInsure's Frequently Asked Questions (PDF).
Media Liability Insurance (Authors Guild). The Guild has an agreement with AxisPro to offer its members professional liability insurance (through the insurance brokerage firm, John Buttine, Inc.). Download the FAQ for more details and see application form for Axis Pro's WriteInsure liability policy, for three covered activities: freelance writing (including commentary on third party websites and blogs), book authorship, and/or your own blog.
SPJ offers access to insurance and financial services through consultants Harry W. Riley III and David N. Brown. Also offers life insurance through MetLife.
Publiability. Mike Mansell (Granite Insurance Brokers) specializing in media liability insurance for publishers since 1977
Affordable media liability insurance is available for members of the National Federation of Press Women (through Walterry Insurance Brokers). Walterry offers Chubb's MediGuard errors and omissions liability insurance for broadcasters as well as for newspaper publishers.
AxisPro's Loss Prevention Guide (this PDF booklet provides basic info on defamation, defamation, invasion of privacy (more complex than you might expect), trademark infringement, and copyright infringement).
MusicPro Insurance (for instruments and computer equipment)
Comment below if anything useful is missing.