Is there a Twitter client (or just a utility) that pushes real time Twitter feed / mentions notifications? By real time, I mean notified as soon as the tweet is posted, like what MetroTwit does in Windows.
Try Polly, I think it's brilliant. Don't know whether it's real time but it's quick enough for me to not notice.
The launchpad site is here Polly.
Or this is the PPA: ppa:conscioususer/polly-unstable
Just to note: It's currently in Alpha development stage but I haven't noticed any bugs as of yet.
The Twitter Notifier extension for Chrome shows real time HTML5 desktop notifications.