There are multiple actions in which I don't think have been reported (as far as I have searched),
As far as these actions goes, I will separate them into two different categories: Actions in which can be done whilst using a sprint key, and Actions that can be done whilst in a boat.

Note:
Said actions must be done after pressing the sprint key or using the "double tap" method. Doing said action allows the player to achieve said action while sprinting and then continue on with playing. Not canceling any sprinting the player has been doing. It's as if the player is able to sprint, do the following actions, and continue on after stopping the action or letting the action finish.

Actions in which can be done using a sprint key include:

• Ducking.
• Eating.
• Blocking with a shield in main hand or off-hand.
• Using a bow or crossbow.
• Throwing a Trident.
• Navigating using a boat.
• Drinking a potion.
• Riding a horse.
• Riding a minecart.

Actions in which can be done whilst in a boat:
Note: You can only do these actions before starting to navigate with the boat.
I.E. you can eat a porkchop, and while the animation is playing, continue to navigate using the boat.

• Eating.
• Blocking with a shield in main hand or off-hand. (Seeing as you can only do said action before starting to navigate with the boat, I see this as a bug.)
• Using a bow or crossbow. (As said above)
• Throwing a Trident.
• Drinking a potion.
• Using an Eye of Ender.
• Sprinting.

Some other bugs/strange behavior I have found while playing:
Player is able to shoot him/herself while sitting in a boat, looking straight down, and firing a bow at full power. The boat will not break and the player will take damage respective to the bow's damage. I have found that this is similar to aiming straight up and firing an arrow and waiting for it to hit yourself. I do not know if crossbows behave the same.