Leaf burn in pepper plants can occur for myriad reasons, including environmental stress and infectious diseases.
The infections which cause leaf burn, almost always leave distinct patterns on the affected leaves, which are noticeably different from leaf burns caused by environmental reasons. See here the damage pattern due to bacterial infection. These burns appear as spots in the inner regions of the leaves, and then they spread. On the other hand, burns due environmental stress start from the peripheries of the leaves, and progress inwards. Older leaves are more likely to get affected by environmental stress. And, the affected leaf parts are dry.
The dryness of the burned portions is important. Because water-soaked burn spots are a telltale symptom of a devastating fungal disease, aptly named as the blight, whose only treatment is to uproot the affected plant and burn it completely, taking care not to infect other nearby plants in the process. Only if the infection is very small, the plant can be saved by excising off a considerable portion of the plant including the diseased area and then burning or disposing off in somewhere far from other plants. Notice here the pattern of leaf burn for pepper blight: the burn progressing in a circular fashion from a defined center. On the other hand, burns caused by environmental factors start at the edge of leaves and then slowly progress inwards without such clear circular patterns.
From your pictures, I think it is safe to remove infections as probable causes. This leaves environmental factors as the reasons behind them. Now, environmental stress can be caused by so many things: overwatering, underwatering, too much nutrients, lack of nutrients, too much sunlight, lack of sunlight, anything or a combination of them can be the underlying cause. As you described, the affected plants are not taken care of that well. I suspect in your particular case, the burns might be caused by either lack of nutrients or too much moisture in the soil or the surrounding.
However, the upshot of leaf burns caused due to environmental stress is that they are slow-progressing, affect older leaves principally, are rarely fatal and may stop when the underlying stress factors are removed. So, it is up to you how much care you would like to take of your plants to prevent leaf burns. The other plants not suffering from burns may be due to them being of different species, and having different levels of capabilities of withstanding the environmental stresses.