Salam Alaykum,
The video is good but I guess it is introductory, because of course there are many issues could be looked into: One is perhaps a further discussion of the view mentioned about everyone literally being the slave of the Prophet (Salla Allahu Alayhi Wa Sallam) and 'Ali (RAA).
Another thing I have not seen discussed by our Sunni side is the supposed 'transition period' between the Ghadir Khumm pronouncement and the passing of the Prophet (Salla Allahu Alayhi Wa Sallam).
That is, taking the Twelvers at their claim, we would say that fine, the declaration would be analogous to an 'election victory' nowadays, but there is a transition period between that and the 'assumption of the office' itself. It is incoherent to say that the Prophet (Salla Allahu Alayhi Wa Sallam) would not have overseen and planned carefully for this transition period of at least a few months, so that the appointment could proceed smoothly into the assumption of leadership itself.
Yes, the Twelvers bring the issue of Usamah's (RA) Army, but this seems a very forced and wishful rereading of events, since no rational person would put all his plans on hoping that only 2 or 3 days before his death the city will be emptied so that a coup in favor of whom he wishes to succeed him can take place (again imagining that the Twelvers are right in saying that 'Ali (RAA) would have stayed back), so it is very strange that they ascribe this to the Prophet (Salla Allahu Alayhi Wa Sallam).
There are perhaps other things, but these were some of the salient ones.