She's basically saying we ought to have some quality-control measures in place so we "reject the rejects". Sounds good in theory - but how do you really implement this? Do you just deny entry to anyone from "Afghanistan, South Korea, Vietnam, Haiti, South Africa, Ethiopia and Mexico"? Do you require those who enter to have college degrees? Do you have an upper-age cutoff? I get her frustration. I just don't see how you can really do much from a policy perspective to prevent the entry of rotten individuals.
I'd definitely support legislation that simply kicks bad apples out of the country for, say, their first five years in country. When she writes "Tapia was still in this country despite having been arrested at least a dozen times on weapons and assault charges.", that's just infuriating.

Other thoughts:
The biggest area I see abused is student visas.
I think in the past, outsiders viewed America as the land of opportunity. They couldn't wait to get here so they could start working, earn what they kept, become upwardly mobile, and maybe even own a business later in life.
Now outsiders view America as the land of getting something for nothing.
If we would stop giving away something for nothing, this immigration problem would largely self-correct.