Christopher Ricks includes this song under the vice of sloth in his Dylan’s Vision of Sin.  Yes, I see where the singer is, just sitting and watching while the river does a great deal more with its flowing.  But I think such a view is the kind we associate with Hamlet who we often think doesn’t do much than contemplate why he can’t murder his uncle, yet he is full of action during the play, what with inserting passages for the “Mousetrap” play, having Rosencrantz and Guildenstern killed, jumping on pirate ships, etc., but our image of Hamlet is either sitting on some precipice contemplating suicide or holding a skull and ruminating about the past.

The singer in “Watching” is also active.  In the first verse he walks to and fro beneath the moon.  In verse two, he shares that the day before he saw someone on the street “who just couldn’t help but cry.” That same day it was someone who was “really shook” that he saw (yes, could be the same person). These are not the experiences of someone who always wants to be stuck on a bank of sand.  He also was in an “all-night cafe.”

Now there is the commitment to watching the river flow as long as it does flow:

But this ol’ river keeps on rollin’, though
No matter what gets in the way and which way the wind does blow
And as long as it does I’ll just sit here
And watch the river flow