Dick Costolo's moment of truth: Twitter investor day

Twitter's investor day is a "watershed moment" for the company, says SunTrust Robinson Humphrey analyst Robert Peck. On the heels of third-quarter results that fell short of expectations and slowing user growth, investors want to hear CEO Dick Costolo lay out a clear, convincing strategy.

And they want to hear from CFO Anthony Noto a plan to close the monetization gap with Facebook. Twitter's stock will swing in one direction or the other depending on how Wall Street receives the comments. And with questions about management upheaval, if Costolo disappoints on stage, pressure could mount to show him the door.

Twitter CEO Dick Costolo takes a photo with his smartphone at the Twitter IPO launch.

Adam Jeffery | CNBC

Here some key issues that will be in focus in Twitter's presentations to investors:

1) What's Costolo's vision for Twitter's future?

Is Twitter a global town square, as Costolo explained at the company's IPO? Or is it a Venn diagram of concentric circles of people who Tweet and people who see Tweets, as he laid out at its most recent earnings?

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Investors want to be clear on what role the company could play in the media landscape, Costolo has talked quite a bit about changing the format to make it more appealing to new users even if it doesn't convince them to log in. Changes to the product have been gradual—are more coming?

2) How can Costolo rev up user growth?

The company's fourth-quarter guidance implies that user growth will continue to slow.

Bank of America analyst Justin Post notes that the company added just 13 million users this past quarter compared with 40 million in the year-earlier quarter, hoping for details on product initiatives to drive faster monthly active user growth and more widespread user content contribution.

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3) How can Twitter make more money from its users without alienating them with ads?

Twitter has to make more money from its core user base, without alienating them with too many ads, and has to figure out how to make money from those people who see tweets but don't log in.

Citi analyst Mark May notes that Facebook was about three times as profitable as Twitter when it was at a similar run rate as Twitter is at, raising questions of how quickly it can grow margins: "Investors will look for more color on areas of investment and plans to balance growth and profitability in 2015 and beyond."

4) Is Twitter's management team stable?

A wide range of senior executives have left Twitter just this year, including COO Ali Rowghani, Product VP Michael Sippey, SVP of Engineering Chris Fry, head of North American media Chloe Sladden, head of news Vivian Schiller and data analytics lead Adam Kinney.

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That much turnover raises questions about whether management has a consistent strategy and whether key employees have concerns about Twitter's future. Citi's May writes: "Investors will want to gain comfort that the changes are not reflective of internal disorder and are constructive vs. disruptive to executing its new growth strategies."