The general comes with a generic AT-ST card. Any idea why this is? Can you field him as a generic in tournament play? Otherwise, why would he have the card?

There's a small bag in the expansion kit with a few pieces that you can sub in for the General Weiss climbing out the top, and the massive guns on either side. If you choose, you can use the other kit pieces and make a standard AT-ST, which the card will then be useful for.

Couldn't you put the generic in the open groups for campaign play?

Ah, didn't pay close enough attention. I see that now. Thanks. Clever, FFG, clever...

Couldn't you put the generic in the open groups for campaign play?

No you cannot. The box set comes with a generic AT-ST already, and in the campaign, you are limited to a single core box set's contents when choosing open groups.

"Component Limitations", RRG, Page 8:

In a campaign, players are limited to the number of figures included in the game. For example, the Imperial player is limited to six regular and three elite Stormtrooper figures, even if he owns multiple copies of the game.

You can, however, use it to field 2 Elite AT-STs in skirmish...