I don't think Twitter is doing "that" badly. It's a popular social network that loads of people rely on daily, and they are making some money, at least.
Either way, I'd make the following changes:
1. Open up the ecosystem again, and take advantage of the recent trend towards data science. Twitter have acquired a lot of startups relating to Twitter analytics, and to be honest I'd push to keep them separate, but a part of the company as a whole. Allow end-users to work with TV analytics, set up news aggregators powered by Twitter analytics, and push them as separate products on their platform. Twitter can separate themselves from the pack by being the ecosystem of choice for developers, and while it won't necessarily mean more money, it creates real value for their platform.
2. Add a cost to verified profiles. Nowadays, even people that work for magazines get a verified profile, because it's been pushed for by their sales department that deal with these people, and it provides otherwise ordinary people premium features. I'd create an "approved profile" flag to allow those that simply want to prove that they are who they are (i.e. press people, and moderately known people that may want to speak to everyone) and make verified profiles a paid-for feature for celebrities that want to ensure that the general population cannot contact them. Set this as a rolling cost per-month, and I think Twitter would make a fair bit of money from those that want to use its platform for commercial gain.
3. Drastically cut their costs by cutting sales/marketing. These departments are huge, and I think Twitter grew them out with the idea that they were going to become a media company themselves. Rather than make redundancies, I'd offer an opportunity for departments to separate from the main company and link up with outside investment, with the promise of access to the parts of the ecosystem they require.
4. Make a bigger deal of live events (i.e. sport, live shows, etc), but do it in a way that keeps them separate from the main product. This links to #3 in that a sales department that purely handles sport contracts could spin off into a separate service that utilises Twitter purely for sports events. Let people extend their Twitter profile on a separate site to indicate their sporting preferences, and allow Twitter to cater the experience for them. For example, I'm a Bristol City fan, so I could sign up to Twitter Sports as a Bristol City fan, and see highlights from the main Bristol City account, the trending hashtags around Bristol City, watch live games, and see what other Championship teams are up to. Essentially, it's making a more localised platform around sports.