Why would Moshe ask Hashem, "Al teifen el minchasam" -- were Dasan and Aviram or Korach going to offer a korban mincha?
Rashi writes that Moshe was asking Hashem to not count Dasan and Aviram's portion of the korban tamid, which was a korban tzibur. (It seems from this Rashi that the korban tzibur was a type of large shutfus, a partnership among all members of Klal Yisrael, such that an individual share could be excluded. See Ramban at the beginning of VaYikra who discusses whether this is indeed the case, or whether a tzibur is a whole that transcends its individual parts and cannot be sliced and diced.)
Ramban takes a more expansive view and writes that Moshe was asking that Hashem not accept any offering or respond to any tefilah from Korach's lot. Why should the fact that these evildoers happened to be engaged in a rebellion against Moshe automatically negate the value of their korbanos? If someone, for example, does not keep Shabbos properly, who are we to ask G-d not to accept that person's tefilah should they come to shul? The difference is, explains Ramban, that the korbanos here would serve as a means to further rebellion. What better way to demonstrate the valdity of a "kehunah for all" popularist rebellion than to lead the masses is offering korbanos without the aid of Aharon or his family? Unfortunately, the baby must be thrown out with the bathwater when the validation of good behavior might be misinterpreted (or where it is deliberately used as a means of fostering the misinterpretation) as validation of other wrong behaviors. This point has practical relavance in other contexts, e.g. can we work together with members of other "movements" of Judaism to achieve shared aims, and if we do, how do we ensure that cooperation in one context is not taken as a broader tacit approval of everything those movements represent? Where do you draw the line?
Seforno goes a step further and writes that Moshe asked that Hashem not accept even korbanos Korach's camp may have offered for the sake of achieving kaparah. Avodah can help achieve repentance in the realm of bein adam la'Makom, but sins bein adam l'chaveiro require asking and receiving mechilah on the part of the one who was wronged. Moshe was not willing to let Korach's lot off with a korban offering alone when it was he as well as G-d who was wronged. I was a bit taken aback by this Seforno. Would Moshe callously deny mechila? I think the point here is that Korach's rebellion at heart was aimed at separating adherence to G-d from adherence to Moshe's leadership. We're all good Jews, preached Korach, and so why should we bow to Moshe's leadership? The only way to undo Korach's false ideology is to acknowledge that no kapparah is possible -- no korbanos are acceptable -- so long as Moshe, G-d's chosen leader, is shut out. The bein adam laMakom is inseperable from the bein adam l'chaveiro of accepting Moshe's authority.
Finally, my favorite reading of this difficult pasuk is found in Ralbag, who suggests that it is not a request by Moshe, but simply a statement of fact -- if those who join with Korach pray that G-d help their cause, G-d will not respond to those tefilos. You cannot daven for G-d's help to achieve an unjust or improper cause -- it just won't work. I seem to recall that the gemara says that even a thief offers tefilah on the threshold of the home he is breaking into. We seem to think that prayer is just another part of the effort required to get what we really want. The thief wants his money, Korach's wanted kehunah, we all want something, and we put those wants into tefilah. What the Ralbag is reminding us is that tefilah works only as an expression of our ethical consciousness -- we pray to bring G-d into the world to make it a better place, not to satisfy our own selfish needs.