Ooh, I like this question.
1. Trim the fat. Reduce the number of employees dramatically. Obviously not a graceful change but I feel there should not be that as many people working there as there are now.
2. Focus on engagement, not growth. Twitter may not be growing in the way that the market wants, but the users that it does have are incredibly devoted to the platform. If I were to leave Twitter there's nowhere else I could go. If I leave Tinder or Snapchat there are many other platforms that can fill almost the same niche. Twitter needs to capitalize on that.
3. Make brands pay to have a page. In other words, if you're not an individual, you must pay to create an account. Savvy companies have realized that being on Twitter is a key part of a solid social media campaign. To not be on Twitter is to miss out on a huge opportunity to reach a very devoted audience, and you can't reach that audience anywhere else (#2). Some brands are already doing this well (e.g. Wendy's.) If the choice comes to paying for the opportunity to market on Twitter, and not market at all, companies will gladly pay. On the plus side, this could let Twitter reduce the interstitial ads on the timeline.
Everyone hates ads, but the way that brands have engaged with individuals on Twitter really humanizes them and makes people form more real relationships with them. It also forces brands to be more accountable and aware.
4. Bring back Vine. A huge part of Twitter's staying power is the unique culture it has created (#2). Staying power is what gives Twitter its greatest value to advertisers (#3).
5. Ramp up engagement on Periscope. Periscope being a part of Twitter makes a lot of sense because Twitter is all about stuff happening live. It's a great platform but I think it also needs a desktop client (with OBS support, the way Twitch does) to allow the caliber of content creation to go up.
6. Re-open APIs. Twitter has sown a bad seed with the dev community by making its API very restricted. Tweets make up a very interesting dataset on which other people could build very unique things on top of. Twitter should encourage this, not stifle it. "Look what cool things we can do with Twitter" will only serve to strengthen the image of Twitter as a unique, irreplaceable platform.
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These are the main issues I see as an everyday user of Twitter. Things like live sports/TV are good ways to grow but these are all secondary to Twitter strengthening its core platform for longevity and meaningful sustainability.