There are a number of changes I would bring the the Twitter platform if I had control.
The first thing I would do is give people the ability to turn off DMs because I don't like getting messages when people follow me after I follow back.
The other thing I will do is fix the link display. When I post links to this blog post, it doesn't display it graphically. Some sites are displayed graphically, but not my blog posts.
I would also add a feature that allows the platform to go beyond the feed, perhaps a TV pane could appear while you are watching TV. A little Twitter feed pane floating in the corner of the TV screen. Twitter gadgets is the word. I would make little gadgets that connects to Twitter, like a key chain with a Tamagotchi appearance that reeds your Twitter feed.
I would also add a Bluetooth feature to Twitter so you can follow people that are physically near to you and learn from them. I could be at work and the bluetooth of my phone would detect colleagues nearby and you could follow them on twitter.
There are other things I would do but I don't want to go on.