"Company" is a broad word, and can include a wide variety of different types of organizations - but if you're talking specifically about startups, look at the following:
Cash in the Bank / Burn Rate - How much cash does the company have? How much of that cash is it spending each month? How long until the company reaches profitability? Could the company be profitable now if it wanted to be?
Headcount - LinkedIn actually tracks this now. How has the total headcount of the company changed over time, particularly recently? Headcount is certainly not a measure of success, but a significant decrease in headcount may be a red flag.
Growth Rate - How fast is the company growing? Ideally you're looking at this in terms of revenue.
Unit Economics - Even if the company is growing, is it making money from every sale? Or is it "spending $1 to earn $0.95" ? Getting a handle on the bottoms-up unit economics of whatever the company is selling is important to really getting a picture of its overall health.
Grit of the Founders - This may be more important than everything else on the list! Every startup is going to feel - frequently - like it's in "bad health." Founders with determination, grit, and the ability to fight through the tough times will overcome a lot of the problems presented by other items on this list.