This fall, Apple chief executive Tim Cook formally apologized for the company’s mistake-filled mobile map application, which became a national joke for its screwy geography. The misstep focused new attention on the legendary company and how it has fared since the death of Steve Jobs in October 2011. Questions abound: Will holiday shoppers fill their carts, virtual and real, with as many Apple products as last year? Is the company’s future as bright as its past? Judging by its stock price of late, investors seem uncertain. Here’s a look at what some are saying in the post-Jobs era and why those perceptions might need some fine-tuning:

1. Without Jobs, Apple doesn’t know how to think outside the box.

Everyone says it: Cook is a staid, sober businessman, while his famous predecessor was a frenetic genius. To some extent, that’s true. Cook has a reputation for not losing his cool; he shows his frustration through a steely, penetrating disappointment (which can be just as terrifying as anger, according to those who have watched both Cook and Jobs in action). But Apple’s current chief executive is far from by-the-book. To think otherwise ignores his greatest strength.

Cook is known as a supply-chain guru, and that represents a kind of outside-the-box thinking that has as much to do with Apple’s success as its innovative designs. Cook joined Apple in 1998, at the beginning of its astonishing climb. Jobs told a BusinessWeek editor in a 2004 interview, “After Tim came on board, we basically reinvented the logistics of the PC business.” Streamlining inventory storage doesn’t have the same cachet as coming up with a sleek, simple design of the iPod, but Jobs was well aware of Cook’s role in making Apple into the dynamo that nearly everyone admires.

The worry remains that, if anything, Apple is now locked in a box of its own making, since relentless innovation is now seen as a trademark characteristic of Jobs, and not necessarily the company. If Apple doesn’t come out with new and daring products, then it risks the perception that it’s losing its edge.

Thus far, though, Cook hasn’t stood still. Apple’s iPad mini, for instance, is risky because it may have lower-than-average gross margins, and it could end up stealing sales from the highly popular iPad, but it certainly shows a determination not to remain rooted in what has worked before.

2. Apple’s innovation days are numbered.

This is related to the first myth, but with a slight difference: It deals with the perception that Apple will have trouble creating anything truly surprising. At first glance, there seems to be some validity to this misconception. But declaring that Apple has reached its innovation peak ignores the larger picture of what it’s trying to accomplish with its desktop and mobile product lines.

Apple’s latest operating system for mobile devices (iOS6) includes Passbook, a wallet application that’s incredibly useful (it is now my default payment method at Starbucks, for instance), and plants the seeds for Apple to become a massive mobile-payment provider. Not as sexy as the iPad, but from a business standpoint, it might represent a huge leap forward. And the much-criticized Maps app, while not necessarily a move for the better in its first incarnation, nonetheless could lead to significant innovation down the road.

Remember, too, that it’s hard to be surprising when everyone is watching and speculating on your next move. Unlike the good old days of the iPod, there’s almost no chance that a new Apple product will make it to market without some advance warning. That has the effect of making everything seem expected, even when it’s often quite innovative.

3. Apple wants to control everything – still.

A common complaint from the Android camp is that Apple’s “walled garden” approach limits users’ ability to control their devices and choose their services. That’s partially true. But there’s another side to the story. Apple’s rules for products in its application store have created the best selection of apps of any mobile operating system. Quality developers flock to Apple’s system as a first resort, knowing that it offers the best platform for actually making money from their apps. The result: Consumers have a greater choice of services, even if they can’t use them as closely with their device’s core features as they might like.

On the hardware side, Apple also offers benefits in return for the limitations it imposes. Building “closed” devices – you can’t open the iPad, for example, to access its innards – allows Apple to push the envelope on device battery life, weight and size. It’s a trade-off, and it’s probably the one that generates the most heat among consumers.

4. Apple doesn’t truly care about working conditions at the plants in Asia that produce its products.

Whether it’s public pressure or the change in the company’s leadership – or perhaps a combination of the two – Apple has taken a major role this past year in pushing for improvements at Foxconn plants in China, the primary makers of iPods and iPads.

The company responded after auditors from the Fair Labor Association, an industry group whose members include Apple, found numerous violations in their investigation of working conditions at the plants – which also have contracts with most of the leading U.S. computer manufacturers. Apple, because of its high profile, is often singled out by labor and human rights groups as a noteworthy offender. It’s the price of being one of the world’s most successful companies.

That said, Apple is not a crusader for social justice, either – it’s a for-profit enterprise that makes a lot of its money thanks to low-cost, high-efficiency assembly in Asian facilities.

5. Apple’s growth isn’t sustainable.

Apple’s stock price has continually increased over the past decade, and despite a decline in 2012, many analysts predict that it will go higher still. But naysayers believe that the stock price, and the rising profits the company reports every quarter, can’t keep going forever.

Predicting the future is always dangerous. But even if we grant that Apple has reached a saturation point in its prime markets (though Mac and iPhone sales continue to grow), consider the opportunities in the developing world and emerging economies. Apple’s sales in China are only beginning their upward arc; China Mobile, the nation’s largest carrier by number of subscribers, has yet to (officially) offer the iPhone.

Growth opportunities still abound for Apple, at home and abroad – and that’s counting only existing products, without even taking into account the company’s track record for coming up with something new and innovative.