Up until now, we had always thought the question was answered and no was no longer in doubt.  One need not exhaust all appeals before starting a legal malpractice case.  In Grace v Law  
2013 NY Slip Op 05383  Released on July 19, 2013 Appellate Division, Fourth Department  we were surprised to see the 4th department call this a novel point of law.  The answer is still no.
 

"Initially, we reject defendants’ contention that plaintiff waived or abandoned his legal malpractice claim by voluntarily discontinuing what remained of his medical malpractice action and failing to take an appeal from District Court’s November 2010 order dismissing the bulk of his claims. In support of that contention, defendants primarily rely upon this Court’s decision in Rupert v Gates & Adams, P.C. (83 AD3d 1393, 1396), in which we concluded that the plaintiff waived his right to raise certain allegations of legal malpractice in the context of a matrimonial action based upon his execution of a settlement agreement. Specifically, we concluded that, although certain allegations of legal malpractice had merit, Supreme Court in that case "did not err in granting defendants’ motion concerning those alleged errors because they could have been corrected on an appeal from the final judgment in the matrimonial action, and plaintiff consented to the dismissal on the merits of any appeal in the matrimonial action as part of the global settlement resolving a bankruptcy proceeding in which he was involved. In so doing, plaintiff precluded pursuit of the very means by which defendants’ representation of plaintiff in the matrimonial action could have been vindicated . . . We therefore conclude that plaintiff, by virtue of his global settlement, waived the right to raise those shortcomings in this legal malpractice action" (id. [emphasis added]). "

"Although the precise question presented herein appears to be an issue of first impression in New York, we note that several of our sister states have rejected the per se rule advanced by defendants herein (see e.g. MB Indus., LLC v CNA Ins. Co., 74 So 3d 1173, 1176; Hewitt v Allen, 118 Nev 216, 217-218, 43 P3d 345, 345-346; Eastman v Flor-Ohio, Ltd., 744 So 2d 499, 502-504; Segall v Segall, 632 So 2d 76, 78). As has been noted, such a rule would force parties to prosecute potentially meritless appeals to their judicial conclusion in order to preserve their right to commence a malpractice action, thereby increasing the costs of litigation and overburdening the court system (see Eastman, 744 So 2d at 504). The additional time spent to pursue an unlikely appellate remedy could also result in expiration of the statute of limitations on the legal malpractice claim (see MB Indus., 74 So 3d at 1181). Further, requiring parties to exhaust the appellate process prior to commencing a legal malpractice action would discourage settlements and potentially conflict with an injured party’s duty to mitigate damages (see Crestwood Cove Apts. Bus. Trust v Turner, 164 P3d 1247, 1254; Eastman, 744 So 2d at 504). "