Twitter defaults to a mixture of "top" tweets and the live feed, so it often repeats. You used to be able to just get the recent ones by looking at the "Live" tab, but I think they removed this in order to force you to look at their promoted tweets (i.e. ones Twitter gets paid to shove infront of you).
You'll also see tweets again if someone you follow retweets one, so it may look old but it's been recently retweeted.
I rarely use the twitter website, mostly because of how bad their website UI is.