I was recently asked to do the job of handing out the honor of opening and closing the ark during davening on Rosh HaShannah and Yom Kippur and was wondering if there was any halachic significance to getting an honor to open the ark? More importantly, would someone be halachicly forbidden to receive that honor (for instance a Kohen who has married a divorcee)?
The Ba'er Heiteiv and the Mishnah Brurah (Orach Chayim 104, 2 in the BH, 9 in the MB) say
העולם חושבים זה קצת למצוה
that the people consider opening the ark to be somewhat of a mitzvah.
In context, they say that if one is finished with Shmone Esrei and has said the pasuk "Yihyu l'ratzon imrei fi", but has not yet stepped out of position at Oseh Shalom, he can go up to open the ark before taking the steps back, because it's considered something of a mitzvah.
My understanding is that the halachic significance ends there. There is no obligation of opening the ark that the congregation must meet, and there's really no halachic need for the ark to be opened at all (unless the Torah is removed to be read).
Regarding who can do it, that sounds like a policy question, for the rabbi of the community or other decision makers. Does the community want to publicly honor someone who has done X? (The answer could well be "yes"--consider the declaration at the beginning of Yom Kippur welcoming the sinners to pray with the community.)