We had a patron come in this past week who said that he couldn't see well and also couldn't type or use a mouse, but he needed to certify Unemployment Insurance. He asked the staff member to login with his username and password and do this for him, and the staff member was, understandably, uncomfortable doing it.
I feel like patrons who divulge their personal data to us are doing it of their own accord and our privacy responsibility is to not share that information with others without the consent of the patron.
In this particular case, the patron was offering his information and consenting for us to enter it for him. As such, I don't think this violates any privacy agreement we have made as employees of the library.
The part that I worry about is, could this come back on an employee if they are doing a legal filing for a patron and the filing may be fraudulent? I am optimistic by nature and like to think people have good intentions, but the reality is, I know this happens. I wouldn't want to put an employee in a sticky legal position if they filed what might turn out to be a fraudulent claim for someone.
Do you know of similar situations in other libraries and what, if any, legal ramifications there might be for employees who could be caught in the middle of something like this?
At first glance, this question seems simple: what are the possible legal risks to a librarian helping a patron fill out a legal document?
But within this question lies another, slightly more complex issue: when does good customer service become an accommodation for a disability?
This "slightly more complex" consideration is brought up by this part of the member's scenario: "We had a patron come in this past week who said that he couldn't see well...", potentially meaning: the patron could not access the library services (use of the computer and internet) without assistance, because of a disability.
Of course, not every visual limit is a bona fide disability (I have to take off my glasses to read these days, but that does not entitle me, by law, to an accommodation under the ADA). However, a patron requesting help to access a library service due to "low vision" (meaning that patron cannot view the screen even with corrective lenses), is potentially requesting an accommodation.
This is because "low vision" can be "a physical or mental impairment that substantially limits one or more major life activities," (which is the ADA's definition of a disability).
For patrons with "low vision," an ADA accommodation can take many forms aside from a human-powered solution, including:
What accommodations a library chooses to offer to someone needing an accommodation to access library services will vary based on that library's size, type, served population, and (of course) budget.  For some libraries, the "human solution" will be the only one available...which creates dilemmas like the one shown in the member's question.
Okay, let's press "pause" on the ADA aspect (we'll come back to it) and return to the original, simple question: what are the possible legal risks of a librarian helping a patron fill out a legal document?
The risks, of course, are that if the patron is accused of fraud, identity theft, or any other illegal activity based on the form's contents, it could lead to complications for the library (and thus, potentially, the employee).
Of course, most types of crimes based on fraud, false personation, and identity theft turn on the awareness and intent of the involved parties. Basically--and this is a big paraphrase--so long as a person can show they had no awareness or intent to help with a crime, they will have a defense against such an accusation...especially if they are performing the action as part of a duty in their job description.
But how can a library avoid such accusations against its employees in the first place? This is where we take the ADA aspect off "pause," and consider how a library's policies can set firm boundaries for good customer service, while also facilitating accommodations for disability.
How is that done? Many libraries already have a version of this approach, but here's my plain-language version of a policy:
Library employees are here to help patrons use library resources, but librarians and library staff may not interpret, provide guidance, or fill in forms for patrons.
Patrons who need assistance filling in a form or completing a document due to uncertainty about the content are welcome to ask librarians for help locating the instructions or contact information for assistance.
Patrons who need assistance filling in a form or completing a document on the library's computer or other resource as an accommodation for a disability, please alert the Director or [insert alternate, accessible means], so the Library may act on the request per the library's ADA policy.
So, to be clear, my answer to the member's overall question is: to avoid doubt, librarians should never help patrons fill out the answers on legal forms if the help is just part of good customer service. HOWEVER, librarians absolutely can read the content and type substantive answers on a patron's legal forms if the library decides (and documents) that it is providing the assistance as part of a reasonable accommodation for a disability.
When considering employee-powered assistance as a form of accommodation, part of evaluating the request must be consideration of how it can be fulfilled ethically. For instance, a person providing an ADA accommodation as an ASL Interpreter must follow the Registry of Interpreters' Code of Ethics (or other professional association). A person providing an ADA accommodation as a "reader" for a person who is blind or has low vision should not offer guidance or commentary on the content--their role is limited to reading, and perhaps typing, based on verbal prompts from the accommodated party. A person typing because the library's only keyboard is inaccessible to the patron and the library has no dictation software should similarly only type as an accommodation, and not offer comment or guidance. 
Some libraries, looking at the range and requirements for certain types of human-powered accommodations, may decide they do not have the staff capacity to provide such resources. Others will say (and support by well-developed policy): sure, we can do that, here's how.
The important thing, no matter what the decision is, is to keep a record as to why a library employee (or contractor) would assist a patron with filling out and/or submitting a confidential or legal document. Since the only reason should be as an accommodation, that reason should be documented in either the policy (for instance, if the library has a standard service) or as an ad hoc request.
Thank you for a very compassionate and thoughtful question.
 Many thanks as always to the "AskJAN.org" web site, which lists common disabilities and their accommodations, including the definition and accommodations for "low vision," found here as of June 28,2021: https://askjan.org/disabilities/Low-Vision.cfm.
 "Ask the Lawyer" has addressed the various types of libraries’ obligations under the ADA in other answers, such as https://www.wnylrc.org/ask-the-lawyer/raqs/65 and https://www.wnylrc.org/ask-the-lawyer/raqs/142.
 Assistance printing, formatting, duplicating, locating a hyperlink, and in general using library technology in furtherance of completing the form is okay.
 Found at https://rid.org/ethics/code-of-professional-conduct/. Are there any libraries with in-house ASL interpreters? That would be cool.
 The National Foundation for the Blind has a helpful article on this here: https://nfb.org//sites/default/files/images/nfb/publications/fr/fr35/1/fr350105.htm.
 This is why consideration of ADA access is so critical in procurement of library resources. As you will see on most ADA-resource sites (like AskJAN.org), most accommodations these days are powered by technology. Although some still rely on human action (for instance, reading aloud), most do not. A library that factors these needs into procurement decisions (buying larger screens, or adaptable keyboards) will not only model a practical commitment to ensuring access, but will reduce the need for employees to be the mode of accommodation--lowering the risk of viewing and contributing to the completion and submission of confidential/legal documents.