"Now, maybe some of the nutritionists can help with this. How complete is a complete protein? Or, what happens if it is not complete? I know that different incomplete vegetable proteins can be balanced to form a complete mixture, but I don't know how far that needs to go.
"Let's just take an example. Suppose that my body needs 60 grams of protein per day. Now suppose that I consume 30 grams of high-quality complete protein, and another 30 grams of incomplete peanut butter protein. How big of a deal is this?"
These are really important questions, maybe not so much for backpacking, but for thinking about addressing serious malnutrition issues that affect on the order of a billion people worldwide.
In almost all balanced diets that provide a reasonable number of calories, there's also going to be adequate protein to prevent an amino acid deficiency. http://en.wikipedia.org/wiki/Complete_protein and http://en.wikipedia.org/wiki/Protein_combining are useful references that show why this is the case, and discuss the exceptions.
That doesn't necessarily mean it'll be ideal, so back to your question as a backpacking question. As others have pointed out, lysine is often the limiter among incomplete plant proteins, even after they're combined. Peanut butter is a rich source of protein, but it only has about half the amount of lysine that would be ideal (some other nuts are actually ~ ideal). Dairy products, meat and fish, on the other hand, have substantially more lysine than is needed, so they'll more than make up for the relative deficiency in the peanut butter, *even if* you are only meeting your minimum requirement. In principle, some other complete proteins that have ~ the ideal lysine level but not extra wouldn't balance your peanut butter quite as well. In practice, few if any recreational backpackers are ever right on the margin, though. After looking pretty closely at my typical backpacking foods, I've concluded that I am more than safe getting the majority of my protein from plant sources with any potential deficiencies more than balanced by the milk I had on my granola at breakfast and the very small amounts of animal-based protein in other meals more as a flavoring than as a calorie source.