This is a list of the quests that can be completed in the Mushroom Kingdom. I know it's not complete with what you do and what you get, but it's a start :) Some of these give out major EXP. Many are also connecting quests, where completing one will start another.

Endangered Mushking Empire
1. Talk to your job instructor

The Test
1. Talk to Head Security Officer

The Story Behind the Case
1. Talk to Head Security Officer

Exploring Mushroom Forest (1)
1. Talk to Secretary of Domestic Affairs
2. Visit magic Barrier
3. Report findings to Secretary of Magic

Exploring Mushroom Forest (2)
1. Talk to Secretary of Magic

Exploring Mushroom Forest (3)
1. Talk to Scarrs

Killer Mushroom Spores (1)
1. Talk to Scarrs
2. Gather 100 Poison Mushroom Caps
3. Give to Scarrs
4. Receive Killer Mushroom Spore Potion

Killer Mushroom Spores (2)
1. Give ingredients for Killer Mushroom Spore Potion to Scarrs

Killer Mushroom Spores (3)
1. Receive Sample of Killer Mushroom Spore Potion from Scarrs
2. Deliver Potion to Secretary of Magic

Friendship with Bruce
1. Collect Sample of Killer Mushroom Spore Potion
2. Deliver Potion to Bruce in Henesys

Over the Castle Walls (1)
1. Talk to Secretary of Domestic Affairs

Over the Castle Walls (2)
1. Talk to Secretary of Domestic Affairs
2. Visit castle walls
3. Report findings to Secretary Domestic Affairs

Over the Castle Walls (3)
1. Talk to Secretary of Domestic Affairs
2. Collect 100 Intoxicated Pig Tails
3. Deliver to Secretary of Magic
4. Receive Thorn Remover

Over the Castle Walls (4)
1. Receive Thorn Remover from Secretary of Magic
2. Use Thorn Remover on vines around castle

James's Whereabouts (1)
1. Talk to Head Security Officer
2. Find James in a castle tower

James's Whereabouts (2)
1. Talk to James
2. Retrieve Helmet from Helmet Pepe
3. Deliver Helmet to James

James's Whereabouts (3)
1. Help James escape

Stop the Wedding
1. Talk to Mushking
2. Destroy one of each: King Pepe and White Yeti, King Pepe and Gold Yeti, King Pepe and Gray Yeti

Where's Violetta?
1. Find Violetta

The Identity of the Princess
1. Talk to Violetta

The Story of Betrayal
1. Talk to Violetta
2. Defeat Prime Minister

Truth Revealed
1. Talk to Violetta
2. Return and speak to Mushking

The Seal of the Empire
1. Talk to Secretary of Domestic Affairs
2. Defeat Prime Minister
3. Receive Royal Seal of the Mushking Empire
4. Return to Secretary of Domestic Affairs

Sending Provisions (1)
1. Talk to Secretary of Domestic Affairs
2. Gather 200 Destroyed Helmets
3. Return items to Head Security Officer

Sending Provisions (2)
1. Talk to Head Security Officer
2. Collect 200 Broken Spears from Royal Guard Pepes
3. Return to Head Security Officer
Reward: 17800 EXP

King Pepe's Scroll (Repeatable)
1. Talk to Head Security Officer
2. Eliminate the following: 200 Renegade Spores, 200 Poison Mushrooms, 300 Intoxicated Pigs, 400 Helmet Pepes, 400 Royal Guard Pepes
3. Return to Head Security Officer
Reward: 4400 EXP

Eliminating the Rest
1. Rescue Violetta
2. Receive Secret Key
3. Go to Skyscraper 3 and destroy minions
Reward: 1200