Burris seems to be a decent guy, although my impression is that he's decidedly a second-stringer in Illinois politics, having tried to move from lower-profile statewide offices (Controller, AG) to higher offices and failed.
Blago is still the governor until he's removed. I doubt that there has been a big push to invalidate any other official actions he's taken during this period (bill signings, executive branch appointments, etc.), and it's hard to say that the investigation denudes him of his constitutional powers. Thus, on the face of it, it appears that he has the authority to make the appointment. I also don't think that the Secretary of State has the legal authority to reject the appointment, as the certification seems to be a ministerial duty and the law doesn't accord the Secretary of State any role in the selection of the next senator.
On the other hand, the case law seems to suggest that the Senate does have the authority to evaluate the eligibility of its members to serve in the Senate. I haven't gone back and read Powell v. McCormack, in which Adam Clayton Powell (D., Bimini) was expelled from the House, but it has been suggested that it would apply to this situation.
I think the most persuasive argument for not seating him is not a dislike for either him or Blago, but the fact that Blago's apparent attempts to sell Obama's seat has corrupted the entire process, and has prevented people who would have been viable candidates from obtaining the appointment (as, for instance, by their refusal to pay bribes). In that case, the only way to be confident that the appointment will be an honest one is to wipe the slate clean by impeaching Blago, removing him, and then having the Lt. Gov. succeed him and make the appointment.
As for a special election, I have two problems with it. First, it isn't what the statutes call for. Second, and this is related, it seems to be an ad hoc solution to a political problem; I think we're better off if we adhere to established procedures, especially when we're talking about the structure or composition of government.