I've got some crumbling on the wall around my vent and peeling paint. Will drywall compound fix it all?

Old layers of paint have bubbled up, maybe due to moisture around the vent. the vent also has crumbling around it making it difficult to attach a vent cover. I'm not a home fixer type, but I was wondering, if I start mudding around the area is that going to help with the smoothness as well as give something for the vent screws to grab? Or is there something else I should be doing for the cracking parts?