I discovered today that "salient" and "desultory" come from the same root word, the Latin "salire," meaning to jump. That's very interesting to me, considering how modern usage has shifted them into nearly opposite meanings.
Merriam-Webster's first definition of salient is "moving by leaps or springs: jumping." I would say the more common use these days follows from its third definition, "projecting beyond a line, surface, or level," or "standing out conspicuously: prominent." A salient point originally simply meant some kind of projection, often related to military formations or structures, but it has gone from that to being used to describe the main thrust of an argument or discussion. The Free Dictionary suggests synonyms for "salient point" including "essence," "cornerstone," and "focal point," none of which seem related to jumping around!
"Desultory" comes from adding the Latin "de" (from) to salire, i.e. to jump from (something), so think of grasshoppers, not butterflies. Desultores were circus performers who leaped from one galloping horse to another. Dictionary.com's first definition of desultory is "lacking in consistency, constancy, or visible order, disconnected; fitful" and its second definition is "digressing from the main subject; random." I've also heard it used in conversation to simply mean casual, in the context of a dilettante, as in taking a desultory interest in some topic.
Again, de means from or down from (or in some cases, about); it's not a preposition related to opposition, such as contra or adversus. Logically and etymologically, desultory should not be an antonym of salient, despite how their usages seem to be evolving in opposite directions. But then, if you crave order and reason in language, I'm afraid that English will often frustrate you; you might want to try instead for being amused by its surprises.