Under US copyright law, there are two questions that must be answered:
- is the book is a work of joint authorship?
- do the editor's contributions qualify as "work made for hire"?
For Bob to have a copyright interest in the work, the answer to the first question must be "yes" and to the second, "no."
On the question of joint authorship, see these model jury instructions from the ninth circuit:
A copyright owner is entitled to exclude others from copying a joint work. A joint work is a work prepared by two or more authors. At the time of the joint work’s creation, a joint work must have two or more authors, and:
each author must have made a substantial and valuable contribution to the work;
each author must have intended that [his] [or] [her] contribution be merged into inseparable or interdependent parts of a unitary whole; and
each author must have contributed material to the joint work which could have been independently copyrighted.
Each author of a joint work shares an undivided interest in the entire joint work. A copyright owner in a joint work may enforce the right to exclude others in an action for copyright infringement.
Note the third point. Catching spelling and grammar mistakes probably does not rise to the level of "could have been independently copyrighted." Rewording might. This would likely require a factual determination (by a jury, or by a judge in a bench trial; more abstractly, the "finder of fact").
As to the second point, it's conceivable that the traditional understanding of the editorial relationship (or the parties' particular understanding of their relationship) was inconsistent with the requisite intention, but again this could easily be subject to a factual dispute that would have to be resolved by the finder of fact.
Contrary to another answer and some comments, the fact that the author "hired" the editor does not by itself make the editor's contributions a "work made for hire." This is also a factual determination that depends on several elements. First, there are two categories of work made for hire; the first applies to employees and the second to contractors. For the first, there is an eleven-element test. From the ninth circuit:
If the issue of the employment status of the work’s creator will be decided by the jury, the Supreme Court has suggested an eleven-factor test focusing on whether the creator of a work was an employee or an independent contractor under common-law agency principles. See Cmty. for Creative Non-Violence, 490 U.S. at 751-52. No single factor is determinative. Id. at 752. The following instruction may assist the determination of the employment status of the person creating the work at issue:
Factors Regarding Work for Hire
You should consider the following factors in determining whether the creator of the work in this case was an employee of the [name of party identified]:
The skills required to create the work. The higher the skills required, the more likely the creator was an independent contractor rather than an employee.
The source of the tools or instruments used to create the work. The more the creator had to use his or her own tools or instruments, the more likely the creator was an independent contractor rather than an employee.
The location of where the work was done. The less the creator worked at [name of alleged employer’s work site], the more likely the creator was an independent contractor rather than an employee.
Applicability of employee benefits, like a pension plan or insurance. The more the creator is covered by the benefit plans [name of alleged employer] offers to other employees, the less likely the creator was an independent contractor rather than an employee.
Tax treatment of the creator by [name of alleged employer]. If [name of alleged employer] reported to tax authorities payments to the creator with no withholding or by use of a Form 1099, the more likely the creator was an independent contractor rather than an employee.
Whether the creator had discretion over when and how long to work. The more the creator can control his or her work times, the more likely the creator was an independent contractor rather than an employee.
Whether [name of alleged employer] has the right to assign additional projects to the creator. The more the creator could refuse to accept additional projects unless additional fees were paid, the more likely the creator was an independent contractor rather than an employee.
Duration of the relationship between the parties. The more the creator worked on a project basis for [name of alleged employer], the more likely the creator was an independent contractor rather than an employee.
The method of payment. The more the creator usually works on a commission or onetime-fee basis, the more likely the creator was an independent contractor rather than an employee.
Whether the creator hired (or could have hired) and paid his or her own assistants. The more the creator hires and pays for his or her own assistants, the more likely the creator was an independent contractor rather than an employee.
Whether [name of alleged employer] is a business. If the party that did the hiring is not a business, it is more likely that the creator was an independent contractor rather than an employee.
For a discussion of the weight of any of the eleven Reid factors, see JustMed, Inc. v. Byce, 600 F.3d 1118, 1125-28 (9th Cir. 2010) and Aymes v. Bonelli, 980 F.2d 857, 860-64 (2d Cir.1992).
The hypothetical is silent on many of these factors, but most likely nearly all of them weigh in favor of a determination that Bob is not an employee.
The other category of work made for hire applies to works made by contractors under conditions defined by statute at 17 USC 101. These conditions include "if the parties expressly agree in a written instrument signed by them that the work shall be considered a work made for hire," a condition that is explicitly absent from the hypothetical.
The answer, therefore, is that Bob might have a claim, should he choose to pursue it, but, depending on the nature of his contributions, he might be fairly unlikely to prevail.
