I am pouring piers for an exterior deck soon, but upon digging the holes, I realize/remember that close to the house the earth was dug out and back-filled for the basement. That was 3 years ago, but the earth is still really easy to dig through in some places. It is clay.

My questions are:
(1) is there a way to pack the bottom of the hole to help stabilize it? Fill it repeatedly with water? Beat on it with a 4x4?

(2) I'm thinking of pouring a footer to give some of the piers more stability. I know of a product Bigfoot, but it does not seem to be available in my area. Is it acceptable to make 2 pours, first a wide (16-20") spot at the bottom, then the pier (12") on a second pour? This article (click for link) (http://countryplans.com/foundation/index.html) makes it sound acceptable, if the junction is reinforced with rebar. (That way I could do the footers myself, then do all the piers at once with a truck delivery.)

Any other suggestions?

There is only one word in your writeup that bothers me as an old road and bridge inspector--CLAY. Its usually wet, stays wet and is unstable. If a bridge had to be built on clay, it would be supported on steel pilings, down to a more stable material or rock.
Otherwise a footing of the type you are describing is the correct thing to do. You are spreading the load out over a bigger area resulting in less psi. I'm just not sure the principle will work in clay. Plus the more concrete you place, the more weight you put on the soil/clay.
If it definitely is clay you won't accomplish much trying to compact it. But there are many types of clay. You may have a more stable variety. If you can compact it (4x4 is good), your spread footing may work OK. But don't let it get wet from rain. Backfill as much as you can as soon as you can. Uncompacted dirt cover makes for good concrete curing.
But if it is bad clay that just deforms as you try to compact it, you had better get a professional opinion before making a decision. I'm sure your goal is a stable long lasting job.

Thanks for the reply, smearcase

The clay here can be maddening to work with; it turns to solid as rock when dry, and mush when wet. That said, it does compact very well, so I guess it qualifies as good clay. We have a good grade away from the house, and the footer will be below the frost line (42"), so there should not be excessive moisture down deep.

Although you expressed some caution, I did not get a sense of serious error here, so I think I shall proceed. With caution.

The good drainage is definitely an advantage for you. The deciding factor I think is whether you can get a firm base for the spread footing (with some rebar approx. 2" from the bottom) to rest on. If it will not compact, you need to re-evaluate and one option would be adding piers and spreading the load out some more.
I think you are proceeding in a very professional way, investigating the conditions and doing all you can to deal with them. No error of any kind.

A deck doesn't have that much weight but I think I would rent a skid steer with a auger, or engage someone to bore down to undisturbed earth and put in sonna tube to surface level for concrete pour. A little unexpected expense but less expensive than trying to correct later.

Thanks for the comments and suggestions so far, this helps a lot.

I sounds like efforts to get to undisturbed earth, as well as pouring footers, may be well worth the extra time and expense.

I think my plan (until I get more information) will be to try to get to undisturbed earth if possible. Barring that, if I can get the earth compacted, I will pour generous footers in the places that need it, then pour piers on top of those.