I didn't bother reading since it's linked to a Penn and Teller site. I don't actually consider them an authority on anything but comedy.
1. It only takes a single landfill of size 35mi*35 mi to take all the trash made in the US over the next several decades to come.

And how high do they think it's going to get before trucks can't get up it? And, where do we have an area 35 X 35 miles (1225 sq miles...it sounds nicer when you just give linear dimensions, doesn't it)? Should we just take over Rhode Island? In more practical terms, given that most landfills are about 0.5 sq miles (give or take), you'd need 2500 landfills. And, if it were just one landfill, how do you get all the trash to it? It would definitely be cheaper to take it to a local recycling center than truck it across the country. And what happens after the 30-40 year lifespan of that landfill is over and we need another one? We could get away with using even less space or extend its lifetime even longer if we didn't fill it up with non-biodegradable stuff that could be reused.
2. Landfills can actually be good things. They show an example of a closed subterranean landfill that has a park (or golf course) built over it. The methane emissions from decomposition are harvested to genrate power. The landfill has a superthick, impervious floor that prevents contamination of the water table. It's all good...or so they say.
Uh huh, or it's a disaster waiting to happen. But, they don't become parks and golf courses without a lot more work and money put in. They don't just sprout grass on their own.
http://www.ciwmb.ca.gov/leaCentral/Closure/Revegetate/Part7.htm
Dealing with the settling over time gets pretty expensive too, it's not just a one-time cost and effort.
This site also has some interesting information about landfills and what needs to be done when they are closed to use that land for something else. By the way, how many golf courses do we need?