In my opinion, no, Mods should not have the ability to accept an answer.
Moderators are not expected—and in fact not supposed—to act as arbiters of the correctness of answers to questions, let alone determining which is the "best" answer.
While it's an answer to a different question, Robert Cartaino♦ (Director of Community Development for the Stack Exchange Network) provided a brief but fully on-point answer here which reads in part:
The "accepted answer" feature was never intended to mark which answer is best or even if the answer is correct. It is, simply stated, the answer that the original author found most useful in solving their problem.
That applies to us here as well. While Puzzling differs somewhat from the usual SE model in that, often, our "questions" are puzzle challenges, the above statement remains entirely and exactly fitting for those questions that are in fact actual questions about puzzles and their creation and solving. For those challenge questions, the Accepted answer is the one that the original author found to be the best solution to their puzzle.
The bottom line is that it would be entirely contrary to the SE model for anyone other than the original poster to Accept an answer. It's worth repeating that it's not the role of the Accept checkmark to signify that an answer is "correct"; it's a mechanism for the question's asker (or puzzle's poser) to signify, as they see fit, which answer (if any) they found most worthy of their $\color{green}{\checkmark \small\text{Accept}}$.
I should note that it's part of the unwritten social contract here that the question author provide closure to the question, and give the modest reputation reward to the best answer post, by Accepting an answer. People sometimes look for unanswered questions to try to solve by looking for ones which have no Accepted answer yet, and often answerers feel they deserve the official recognition for successfully solving a puzzle. When I see a question with an answer that is at least plausibly complete and correct, but hasn't been accepted, I personally try to remind the asker to do so—they may have forgotten, or thought they'd done so, or just not noticed the answer, or even simply don't know they should!
We are accustomed to correct answers being Accepted; it's a built-in mechanism to indicate the question author thinks their question or puzzle is addressed to their satisfaction; it provides searchable, visible indication of that fact; and it allows the question author to give a token reward to the answer they felt most deserving. Not accepting an answer suggests the author doesn't think their question is fully addressed or their puzzle fully solved, and/or suggests they found none of the answers worthy of extra reputation.
At the end of the day, it's entirely the prerogative of the question author to decide how (or if) to Accept an answer, and what signals they want to send by exercising that choice. Neither the moderators, nor the community at large, should be able to make it for them.
