Does a grayish/brown color indicate that raw ground beef has begun to spoil?

Not necessarily. When exposed to air, ground beef undergoes a process known as lipid oxidation, which can cause spoilage over an extended period of time and typically is accompanied by discoloration. However, ground beef also may undergo discoloration prior to spoilage and remain perfectly suitable for consumption.
 
Here's how it works: The pigment responsible for the red color in meat is oxymyoglobin, a substance common to all red-blooded animals. Fresh cut meat is purplish in color and remains so if it is  vacuum-packed--and thereby deprived of oxygen--immediately after cutting. Problem is, the majority of consumers don't find the purplish color very appetizing. More frequently, processors or retailers expose meat to oxygen until it “blooms”--or assumes that tell-tale reddish cast --whereupon it is packaged. Often, for purposes of merchandising, product packaging is infused with nitrogen or other gases to slow lipid oxidation and prevent discoloration. That's because consumers associate a grayish/brown color with spoilage or inferior product.
 
Unless product packaging is infused with carbon monoxide – a USDA-approved but rarely used method of sustaining meat's bloom--all ground beef eventually assumes a grayish/brown color. Because color doesn't necessarily distinguish fresh from spoiled product, it's always best to cook the meat within two days of purchase or, again, freeze it.
 
Source(s):
Foodreference.com "Ground Beef Color"