I concur with your points, but have a few corrections to (3) and (4), as the best way to win an argument is to not allow any holes:
The "winner takes all" system means that all of a state's electors are pledged to the winner of the popular vote in that state, regardless of the margin. What happened in 2000 was that Bush won his states by narrower margins than Gore won his states, resulting in the "packing" situation that is the principle argument against an electoral college.
The electors in 2000 all voted as they were assigned. The controversy over Florida's electors was over who to assign them to vote, as the results were within the margin of error for the voting process. If electors were assigned proportionally, the "hanging chad" would have come down to the one odd elector, rather than all 25, and we would never have heard about it.
Separately, I think that (2) is one of the most important points, and the one that is least likely to see attention. I remember my frustration in the run-up to 2008's election to hear Howard Dean in an interview on NPR defend not only the primary system, but having different states vote different ways. If one of the more progressive voices at the time is married to that system, we have a long way to go to change it.