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.