And yet, Sandberg’s boast also highlights a problem. American Idol’s season finale brought in more than $40 million in advertising, according to industry estimates. On a typical day last year, Facebook (FB) took in just $5.6 million or so in the U.S. So conservatively, each set of eyeballs trained on the mewling of contestants on Fox is worth at least 30 times more than those checking in with friends and family on Facebook. And it’s not just television that Facebook lags behind. Every one of its 900 million users generates a little more than $4 in revenue for Facebook in a year. By comparison, Google (GOOG) grosses at least 7 times more from each one of its users. In other words, Facebook makes gobs of money because of its massive reach, not because it is a particularly effective advertising medium.

As Facebook seeks to justify and sustain a mammoth valuation that seems certain to top $100 billion, it faces enormous challenges. First and foremost, the social networking service must find a way to accelerate the growth of its advertising business, which slowed to 45% in the most recent quarter from nearly twice that rate the year before. And it must do so in the face of headwinds from the rapid shift of users from the Web to mobile devices, where Facebook’s monetization efforts are still nascent. In short, for all its promise and its potential to revolutionize entire industries, Facebook must prove to advertisers and investors that it can build a global ad business to match the power of a social networking product that has become a habit for nearly one of every seven people on the planet.

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To be sure, the fact that Facebook’s advertising prowess lags behind its preeminence as a social hub is by design. Zuckerberg has always made the Facebook product his top priority, sometimes at the expense of the company’s ad business. But now that Facebook will be a public company, his team will be under enormous pressure to deliver financial results that keep investors happy. Here are three things he should focus on to achieve that.

No. 1 Advertising
Facebook ads have become table stakes for any online display advertising campaign, but as these ads move from experimental purchases to the cornerstone of many advertising strategies, Facebook must show to advertisers that these spots deliver significant returns.

In the past year, Facebook’s approach to advertising has changed. Now, rather than simply sending salespeople out to sell its ad inventory, Facebook has begun to hire MBA-carrying “relationship managers” with experience in the industries from which the advertisers hale. These folks call their clients “partners” instead of “advertisers” and encourage large bands like Procter & Gamble (PG) to stop chasing “Likes” and, instead, look at what people are actually saying and doing on Facebook that relates to them — engagement. Facebook believes that if brands can jumpstart these conversations on fan pages and within apps they’ll naturally buy more ads.

Facebook attempted to coin new language for this when it launched its latest advertising strategy last February. Advertisers can pay Facebook to highlight “sponsored stories” in users’ Newsfeeds. The idea is that users will only see these sponsored stories when they are posted by a friend or a business with which they’ve already chosen to connect. It sounds great, but the effectiveness of sponsored stories is far from proven. In fact, some brands are questioning the value of advertising on Facebook altogether. GM (GM), which last year spent $10 million with Facebook, decided to stop advertising on the platform because the company’s marketing executives weren’t seeing the impact they desired. Unlike Google, which stumbled on a magic formula with search marketing, Facebook has yet to find its silver bullet.

No. 2 Mobile
Facebook’s users are decamping to mobile devices faster than the social network can keep up. American Facebookers who use the service on both their desktops and on mobile apps are spending more time on their smartphones and tablets — about 7.4 hours each month, according to Comscore (SCOR) — than on the website itself — about 6.5 hours each month.

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This poses two significant challenges for the company. First, mobile screens are small so Facebook users see fewer ads. This unsettling trend is disproportionately impacting some of Facebook’s most important advertising markets. In recent regulatory filings, Facebook said the shift is happening fastest in places like the United States, Brazil and India.

Second, even if Facebook can figure out how to serve up more and better mobile ads, the company lags behind its rivals on mobile strategy. Apple (AAPL) and Google make the operating software for the most popular smartphones on the market. It’s possible that over time, Google could integrate its Facebook competitor, Google+, into its Android phones and tablets more seamlessly than Facebook, giving it an advantage with consumers. In the last couple years, Zuckerberg has attempted to forge closer ties with Apple. The companies have held multiple rounds of discussions, according to people with knowledge of the talks. But they have yet to find a compelling way to collaborate, and in the meantime, Apple has chosen to integrate Twitter, rather than Facebook, into its mobile software.

To combat its rivals, Facebook has moved aggressively to acquire mobile assets. Most notably, Facebook recently agreed to purchase the photo-sharing app Instagram for $1 billion. The company will get a fast-growing product with tons of users and — perhaps more importantly — a pool of talented programmers experienced in designing for handheld devices. The sale isn’t expected to close, according to recent regulatory filings, until later this year.

No. 3 China
Call it Facebook’s black hole: The world’s biggest social network, as of now, has no presence in China. With some 500 million people online, China is the world’s largest Internet market by number of users. About half of those users are active on locally grown social networks. It’s a vast and potentially lucrative market for Facebook, but for the time being it’s likely to remain elusive.

Zuckerberg’s interest in China is no secret. He has been learning Mandarin and has visited the country on various occasions, most recently in March, when he traveled to Shanghai with his Chinese-American girlfriend, Priscilla Chan. Inside Facebook, Zuckerberg’s has led intense discussions among senior management on the risks and rewards of going into the Chinese market, according to people familiar with the situation. And he has held discussions with various Chinese Internet companies, including search giant Baidu, to explore potential joint ventures, which would almost certainly be required for Facebook to be allowed to operate in the country.

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Zuckerberg is also said to be eyeing China as a source of talented engineers. In recent months, however, the internal and external discussions about China have died down as the attention of Facebook’s senior brass has been focused on the I.P.O., the people familiar with the discussions said. In its I.P.O. prospectus, Facebook acknowledged the obvious, saying the Chinese market “has substantial legal and regulatory complexities,” but that the company will “continue to evaluate entering China.”

For now, Facebook is likely to focus its international expansion efforts in countries like Japan and South Korea, where it is struggling to compete with local rivals, and emerging markets like India and Brazil, where Facebook has made significant inroads but has lots of room to grow. Down the line, Zuckerberg and Co. will no doubt try to formulate a China strategy. Whether it will ever pay off is an open question. After all, it’s the Chinese government, not Facebook, that will have final say on whether Facebook can enter the market there. That leaves investors thinking of China as potential bonus whose value may never be realized. “I’m not paying anything for China,” says Lou Kerner, founder of the Social Internet Fund, which invests in private shares of social and mobile companies.

— with reporting by Alex Konrad