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I tried to make a note on my watch but it just requested that I use handoff. I took that as a NO, they don't allow you to make a note or see notes. I hope that you can in further updates!
 
I only used the note app as sort of clipboard to copy -> edit -> copy -> paste things/drafts. I'm a bit curious what task is it doing for you?
 
Reminders is much better for grocery list. You can't do reminders on the watch at the moment either but hope it comes.

Reminders: You can get the reminder alert and you can use Siri to create a new reminder but you can't scroll through a list (like Shopping) yet and I hope I am able soon.
 
Reminders is much better for grocery list. You can't do reminders on the watch at the moment either but hope it comes.

Reminders: You can get the reminder alert and you can use Siri to create a new reminder but you can't scroll through a list (like Shopping) yet and I hope I am able soon.

I can confirm that. I shared a reminder list with my girlfirend. Very handy because we both can add tasks & mark them as complete.

You can also use Siri to add tasks:
http://www.imore.com/how-create-and-share-shopping-list-siri-and-reminders-app

And if you want to share it with another person:
http://www.iphonefaq.org/archives/974042
 
Doesn't help you but I use MS OneNote for all my notes across all devices/platforms.

Can see those notes on the Watch
 
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