In New York there is case law which holds the attorney liabile for errors by a process server. Here is a similar case and analysis from Arizona

"Like most states, Arizona recognizes an exception to this rule, generally referred to as the "nondelegable duty exception." Id. "The policy reasons justifying such a departure are that the employer is the one who primarily benefits from the contractor’s work, the employer is free to select the contractor and may insist on one that is financially responsible and competent, and the employer has the ability to internalize the cost of insurance necessary to distribute the risk as a cost of doing business." Miller v. Westcor Ltd. Partnership, 171 Ariz. 387, 391, 831 P.2d 386, 390 (App.1991).

As the Arizona Supreme Court held in Ft. Lowell, the nondelegable duty exception arises in situations involving a "special relationship between persons," such as "persons who engage in relationships that are ‘protective by nature’ (e.g., the common carrier, innkeeper, employer) [who] are often held to possess an affirmative duty to guard the safety of their respective charges." Ft. Lowell, 101, 800 P.2d at 967. The Court explained:

The nondelegable duty exception is somewhat of a misnomer because it refers to duties for which the employer must retain responsibility, despite proper delegation to another. Such situations exist where the employer is under a higher duty to some class of persons. This duty may be imposed by statute, by contract, by franchise or charter, or by the common law. If the employer delegates performance of a special duty to an independent contractor and the latter is negligent, the employer will remain liable for any resulting injury to the protected class of persons, as if the negligence had been his own. The exception is premised on the principle that certain duties of an employer are of such importance that he may not escape liability merely by delegating performance to another.
The type of situation — i.e., negligence of a process server — was addressed in Kleeman v. Rheingold, 614 N.E.2d 712 (1993), where a client brought a legal malpractice action against a law firm based upon negligence of process server in failing to serve medical malpractice defendant within statute of limitations. The sole issue addressed by the Court was "whether an attorney may be held vicariously liable to his or her client for the negligence of a process server whom the attorney has hired on behalf of that client." Id. at 714. "