Technically what are the four corners of the continental US?  I am
looking for a location name for each.

Generally recognized as the most northwesterly point in the
continental U.S. is a northern Puget Sound beach at Blaine,
Washington, adjoining the Canadian border.  Going clockwise, the other
corners are along the Canadian border at the northern edge of
Madawaska, Maine; a Caribbean beach at Key West, Fla., and at the
westernmost terminus of the Mexican border along the Pacific Ocean
near San Ysidro, Calif.

These points are listed on numerous sites, including the appropriately
named domain below:

Four Corners Motorcycle Tour
http://www.usa4corners.org

Google search term: "four corners" "san ysidro"
://www.google.com/search?hl=es&ie=UTF-8&oe=utf-8&q=%22four+corners%22+%22san+ysidro%22

I used "San Ysidro" as part of the search term because of personal
knowledge that it is unarguably at the southwest corner of the
continental U.S.  I had to do that to exclude the Four Corners region
(where four states meet).

An argument might be made that Cape Flattery on the Olympic Peninsula
of Washington state is at the northwest corner (it's more westerly
than Blaine, but not as far north), and I did find some sites, such as
the following, listing it as the corner.

Cape Flattery Trail
http://www.northolympic.com/capeflatterytrail/readfeedback.html

Google search term: "most northwest point"
://www.google.com/search?q=%22most+northwest+point%22

I suppose that using the same argument it might be possible to name a
point near South Lubac, Maine, as the northeast corner (it's farther
east than Madawaska) and Palm Beach, Fla., as the southeast point
(it's further east than Key West), but I found no references to anyone
making such a claim.

You'll have to look at a map yourself to decide whether Cape Flattery
or Blaine wins the honor for being the northwest corner (personally,
I'd pick Cape Flattery). But you'll find little argument that the
other three corners are at Madawaska, Key West and San Ysidro.

Great response, but not 100% totally clear since no official
clarification was made on two locations, but that is ok, who is
offically going to clarify these details anyway.

I asked this question since I live close to Cape Flattery and the site
you reference below I actually built.  On a side not Cape Alava is the
most western point in the US, by just a few feet.