Is it useful to change the grip between sets? If I'm doing lat pulldown or seated rows, is it helpful to switch from narrow to wide grip between sets? Or am I diluting the value of doing multiple sets of one exercise?
Useful is a very relative term in relation to working out. Varying your grip between sets will change the order in which muscles are activated in order to complete the exercise. For an example, see the article on BodyBuilding.com about the various chin-up grips and their varying strengths and weaknesses.
Changing the pathway you follow to achieve a full repetition will also change the activation order of the muscles, and also activate muscles that you might not normally activate much, if at all.
You won't be diluting the value of doing multiple sets as long as you are still achieving a full range of motion during the exercise, as all the muscles will still be activated, just in varying order and intensity.
That depends on a lot of things. Basically, changing your grip from narrow to wide changes the level of involvement of the different muscles. Changing your grip might be good in that you can hit areas that aren't being targeted enough otherwise in your workout(s) or it could be not so good if you're removing the stress from a major area before it's fully exhausted.
Which of those two is the case is going to depend on your full workout, where your body is physically, etc.
One useful situation for this is when the supporting muscle(s) aren't able to "keep up" with the major muscle in an exercise. You can change an exercise slightly (or move to another exercise) to take the strain off of the supporting muscle(s) while still targeting the major muscle. I hope that makes sense.