Do mayonnaise based foods like potato salad go bad faster than other foods at the barbeque?
First, it's worth reminding ourselves (again) that mayonnaise by itself is usually incapable of supporting the growth of bacteria (or the production of bacterial toxins) because it's composed of mostly oil, with the very small amount of egg yolk which contains ALL of the salt and blended with the ALL the acids, making it inhospitable to bacteria.
Second, let's PLEASE drop the worn-out and meaningless phrase "to go bad"! Most people are confused between "obviously decomposed", or "spoilt" (such as milk that is "sour", or raw meat that is becoming slimy and greenish), and what really deserves your full attention, the INVISIBLE growth of a dangerous pathogen on otherwise fine-looking food. This could be a delicious-tasting ham sandwich that already contains enough Staphylococcus enterotoxin, or Listeria monocytogenes to harm you because it's been contaminated and allowed to incubate at the wrong temperature for sufficient time. But you'd never know it!
Mayonnaise becomes potentially hazardous when it's well-mixed with other foods (such as softened, cooked potato chunks) which allow "gradients" of pH and nutrients that will support any bacterial growth. The bacteria may be harmless spoilage types or they may be pathogens introduced by the other foods, hands, implements, contact surfaces, or even the relatively rare possibility of something from the raw egg yolk. Now you have the problem.... No further "kill step" + various foci in the potato salad where these guys can multiply + food that doesn't immediately change appearance and is expected to be a little sour from the lemon or vinegar.
Bottom line: once mixed with potatoes, etc., mayonnaise becomes a potentially hazardous food (especially if you mixed in the potatoes while still warm). It should have been UNCONTAMINATED, and kept COLD.
But to answer the question directly, once contaminated and warm, mayonnaise-based foods such as potato salad, chicken salad, tuna salad, CAN be almost-perfect growth-media, and probably the first to cause a problem at a BBQ.