Are there ways to tell if sour cream is spoiled?

Yes! It’s a myth that sour cream is already in a “spoiled” state, and therefore “can’t go off.”
 
Sour cream is a fresh, glossy blend of pasteurized cream and lactic-acid-producing bacteria. The term “sour” refers to the bacteria’s tangy, acidic flavor. The following are signs of spoilage caused by oxygen, humidity, bacteria, or poor-quality milk:

• Moldy black, green dots and swirls on the surface
• Blue, pink or yellow bacterial blemishes
• Large amounts of watery whey on the surface of the sour cream
• Strong doughy yeast-spoilage odor and a faint white or pink sheen
• A bitter or “green apple” flavor

 
Source(s):
Dr. Robert Bradley,  professor emeritus of food science, University of Wisconsin

Cary Frye, vice-president of regulatory affairs, International Dairy Foods Association

Handbook of Food Science, Technology, and Engineering by Yiu H. Hui, 2006