They are not out of date, and I'm not at all worried about the consistency, but I would like to know what the specific risk is in eating.  I'm studying food safety and sanitation right now, and the only issue addressed relative to potatoes is baked ones that are improperly stored.

Glad to know you are studying food safety and sanitation. The main issue with potatoes is that they are not acidic, they are a very neutral PH so when combined with dairy it can present real food safety problems, if left out at room temps once cooked. As a general rule, keep food hot, cold food cold and avoid keeping potatoes for any extended amount of time in the danger zone.

Here are some of the Dr. Potato posts on food safety, mostly with potato salads and baked potatoes left out at room temp:

Dr. Potato Food Safety posts

You'll have to refer to the specific manufacturers for tips on the food safety risks. I think most are going to tell you if they are soft and have been that way for a while to toss them. Here are their links: 

Idaho® Potato Processors