There is a midrash discussing Ezra's fixing the text of the Chumash. Where he was unsure of whether a word should be present, he put the word in but put dots over the word. To explain, rather than cross out words, scribes put dots over words they accidentally insert, to note that it should be deleted. We see this in various manuscripts. Ezra's reasoning was that if Eliyahu comes and determines that the word should be there, behold, it is in there. And if he comes and complains that the word should not in fact be in there, behold, there are dots over the word!
Elsewhere, a fairly standard method of derasha is that if there are dots over certain letters (specifically a minority), to interpret the word as if those letters were missing.
This seems like a likely explanation of the dots over Aharon -- that there is some standard variant text in which Aharon is missing. And the grammar would not be harmed by deleting Aharon, for pakad is the singular.
I came to this conclusion before checking any variant text. And then I checked, and what follows are my results.
In the Septuagint, Aharon appears. Thus:
39. πᾶσα ἡ ἐπίσκεψις τῶν *λευιτῶν οὓς ἐπεσκέψατο *μωυσῆς καὶ Aαρων διὰ φωνῆς κυρίου κατὰ δήμους αὐτῶν πᾶν ἀρσενικὸν ἀπὸ μηνιαίου καὶ ἐπάνω δύο καὶ εἴκοσι χιλιάδεςHowever, in the Samaritan Bible, Aharon is indeed missing. Thus, what is pictured to the right. Should we say that this is the "correct" text? No. We should try to evaluate based on other merits, and possibly come to know concrete conclusion, if one is not possible. And that is just what we have in our Masoretic text.
Meanwhile, Rashi notes the dots and explains it based on a gemara in Bechoros. Either he is not familiar with the Samaritan text, or else he is drawn anyway to explain this on traditional, midrashic grounds. Or because this is a fairly old explanation. He writes:
counted by Moses and Aaron: There are dots over the word וְאַהֲרֹן to show that he was not included in the sum of the Levites. [Bech. 4a]That gemara reads:
Thus, this explanation goes back at least to Tannaitic times, and the dots go back to Tannaitic times, which makes sense, given how far back the Samaritan Chumash cropped up.לא קשיא כדמר בריה דרב יוסף משמיה דרבא
דאמר פטר רחם בפטר רחם תלה רחמנא ואהרן שלא היה באותו מנין לא ליפקעדתניא למה נקוד על אהרן שבחומש הפקודים שלא היה באותו מנין
Now, the straightforward reading of Rashi, and of this gemara, is that Aharon was not included in the countees, rather than the counters. This troubles some supercommentaries on Rashi. See Sifsei Chachamim.
Thus, Mizrachi poses this counters / countees issue. And Sifsei Chachamim suggests that Aharon was included in neither. And that was why it bothered to first include it, and then put the dots over it, to be able to teach us this extra point.
I find this unlikely, even within this midrashic explanation. Because there is a difference between giving an extra midrashic twist and making your midrash explicitly contradict a pasuk, and make it a falsehood. By way of comparison, with the dots on Esav's kissing Yaakov, the explanation is put forth that he bit under the guise of kissing. To say that Aharon was nowhere, not even among the counters, is to declare the Torah false. And I do not believe a midrash would do that. Rather, the midrash might be saying that he was there in one respect, namely counting, but there is a pegam in his presence, in that he was not counted.
Update: See also my follow-up post on the implications of my answer of the reason for these dots.