Was the "unrelated subplot" a later development in the show?
I don't think the subplot was usually unrelated; it generally tied in to the main plot at some level and sometimes proved the key to its resolution, it was just more focused on character development.
Samaritan Snare -- with the Enterprise dealing with the Pakleds and Picard dealing with surgery -- was in Season 2. Other well-known examples include The Host (introduction of the Trills), The Most Toys (the crew comes to terms with Data's apparent demise), Hollow Pursuits (Reg Barclay), The Measure of a Man (Picard's past with the JAG officer), Force of Nature (a Data-Spot subplot), and quite famously Yesterday's Enterprise (Yar's subplot) and The Best of Both Worlds (Riker's rivalry with Shelby). That's a very abbreviated list, and I have the feeling a lot of those are from Season 3 or later.
Thanks. It's all lost in the mists of my memory. The ones I saw a week ago seemed unrelated, but I might not have been paying enough attention.