Balgruuf the Greater
Ulfric Stormcloak
and possibly Idgrod Ravencone
Skald is a blind Stormcloak supporter, not to mention his arrogant attitude towards everyone, including the player.
Siddgeir possibly deposed his father by Imperial machinations, is far to arrogant for the little actual experience he has running a hold, and has some form of relations with local bandits.
Igmund is corrupt under Silver-Blood money, and orders guards to ignore the obvious Forsworn threat within the city. He does not escape the Jarl-Arrogance syndrome.
Laila Law-Giver is truly incompetent, seeing Maven Black-Briar as her friend, (ha) ignores reports of Skooma dealings, and blindly puts her trust in her steward. She doesn't even actually run her own damn city.
Elisif the Fair is the Empire's lapdog, and has no real experience to be the High Queen. Balgruuf, and even Ulfric are more fit to lead.
Korir distrusts all magic, which may, or may not have caused the Great Collapse. He blames the College for his failings, when he could be trying to return Winterhold to it's former glory, in one way or another. Instead he pursues relic weapons in a attempt to gain some form of power.
Why the incompetence, Beth?
also, this might be spoilers, so mods, please move if needed.