The spec I'm writing has a guest character (the Patient of the Week) who, from what I've heard, is very much like Tony's mother from The Sopranos. Should I take the time to sit down and watch all the episodes that she was in to make sure I'm not ripping them off?
I don't see why you would. Tony's mom is a type. We may not have seen that type so forcefully portrayed on TV, but she's a type. David Chase doesn't own the mom-as-martyr type any more than Joss Whedon owns Teens With Snappy Banter.
If you haven't seen
Sopranos, you probably won't seem to be ripping off
Sopranos. It's usually the other way around. If you've been immersing yourself in a show, be careful you're not ripping it off too blatantly. I have a very Neil Gaimanesque TV pitch. I had a homeless angel character who was very close to a character from one of his short stories, and I didn't notice. Fortunately my crafty assistant noticed my character was a go-to. I changed the character to something less derivative, and much edgier, and much more original.
Don't worry about influences too much. So long as you're putting a lot of yourself into a script, you won't steal too much from other people. It's when you write too much from other writers, and not enough from yourself, that you get into trouble.