Remember, we don't really vote for President, the electors of the electoral college do. We vote for the electors, now, but that wasn't always the case. In fact even now, it's only a matter of *State* laws, changeable by the legislatures of the several states. And they don't all need to use the same methods.
The Constitution says:
Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.
Appointed!
That's in the "original" body of the Constitution, and was not affected by the 12th amendment, which did change the way the electors voted. (Prior to the 12th, they only voted for President, although each got two votes. The runner up became VP. As you can imagine, that didn't work out too well. There were only 3 Presidents (Washington, Adams, Jefferson, elected under that scheme, before the 12th amendment changed it.
The Constitution further provides that the votes of the electors are delivered to the Senate, where The President of the Senate, that is the current VP, opens them before both chambers. But there is no provision for "validating" the votes, nor for "vetting" the person selected.
Even though traditionally the Chief Justice swears in the President, that's not a Constitutional requirement. In fact LBJ was sworn in by Federal District Judge Sarah T. Hughes,(later to become somewhat infamous as a member of the three judge panel which first heard Roe V. Wade, and as a judicial activist mandating how the Dallas County Jail should be run) ), on Air Force One, sitting on the tarmac in Dallas. (Ironically, she did not know that the oath is specified in the Constitution, fortunately someone else did and they faxed a copy to the aircraft).
Did thye have faxes then ?
Or was this teletype?
Hey, I've taken lessons from Buckhead...