Given the ability of the of the United State's military, why was the evacuation of the capital allowed to fall so deeply into chaos? Was it considered a tactical failure, were their any reprimands for the commanders in charge?
I'd say the evacuation was rather successful given its limitations. Tens of thousands of people made it out of a country that was falling to an invasion from its neighboring state. Not just anyone could resettle in the US -- you had to have reason to believe that the invading North Vietnamese administration would persecute you. This usually meant that you had worked with the RVN government/military or on behalf of the US.
Part of the problem is that unless Washington wanted to publicly abandon its ally in Saigon, it could not withdraw its people or allies in the Republic of Vietnam. Doing so would have meant conceding South Vietnam to the North Vietnamese military. And of course, the whole point of the Paris peace accords was that the United States and South Vietnam were not willing to give up. Prior to capitulation or capture, there can be no evacuation. Moreover, the North Vietnamese offensive -- which violated the peace terms -- came quickly, preventing a long preparation for the evacuation.
Try and put yourself in the mind of those conducting the evacuation.
How exactly do you explain to the people you want covering your ass as you escape that "Ok so here's the plan. You're going to stay here & face the wrath of the NVA while I get on a boat to Hawaii."
You can't because no-one who gets the sorry end of that stick is going to go along. They'll take you hostage & demand to be pulled out. You can't take everyone who wants to leave with you, there aren't enough boats. You can't keep fighting effectively either because congress won't authorize it, the political will is broken.
So you have to give people the idea that they have some hope of getting out if they play along. Which means things inevitably fall apart according to probability & some people who really wanted out or who were supposed to get out get left behind.
As it was all this would have been recognized, there must have been behind the scenes negotiation. As the NVA approached they held off from final seizure of the city for a period. Why? Press a cornered enemy & you'll take unnecessary casualties, people will panic and try to fight their way out.
Wait 24-48-72 hours & the Americans will get all their people out, then leave. As those South Vietnamese Loyalists realize that there isn't the next helicopter or the next ferry coming for them like they were promised they'll do what they did historically. Strip their uniforms & try their best to blend in to the local population while the NVA rolls down the streets peacefully.