"If you're paralyzed and cannot bring an eating utensil to your mouth, should you be put to death?"

I say you should be wise with who you marry, because if your medical science experts determines you can no longer make decisions, then someone has to make decisions for you. To aviod requiring someone else make a decisions for you, you should write a living will. A living will would in my view trump your spouse or any other guardian choices.
If you believe that Terri [as a rational person] who should control her fate, rather the State controlling her fate. Terri's choice was to marry, and marriage is [a sacred] partnership/union.
The question is who chooses? I say Terri chooses. There is no doubt that Terri is no longer capable of making anything that approaches rational decision. If Terri was "merely" insane or suffer from severe dementia, her decison capablity would be in doubt. And therefore her spouse could be required to make decisions for her.

So, instead of "put to death"; it's allowed to die.

"The feeding tube is gone and Terri can breathe on her own. ALSO, she CAN swallow (I've seen it on film and nurses and doctors have said that she can swallow). What, at least, is the harm in letting her swallow some food by mouth? After seven days without nurishment and water, I'd be too tired to hold a spoon."

I don't necessarily agree with her husband's decision, but Terri can no longer make decisions, so the question becomes is her husband sane. Since her husband's sanity does not appear to be in doubt, he therefore makes the decisions as her guardian.
The reverse is also true, if Terri's situation differnet, say she was kept artifically alive in everyway, and was non-responsive or say in agony every second of her life, her husband could make the choice to continue her life indefinitely.

I don't know the particular laws, but I would say that the husband has an obligation to make her decisions and since divorce is a generally mutual act, he couldn't *even* divorce himself out of this responsibility. Though I think he could claim he was incapable of taking this responsibility, and it could pass to next in the legal guardian succession. Additionally on the flipside the continuation of marriage is mutual, if a spouse is no longer there as rational partner, the spouse should not be required to get a divorce, but should be allowed to remarry.
There are of course problems with this, what happen if spouse were only thought to be permanent, but instead recovered. And other issues.