Say if I retweeted everything in my Twitter stream, is there a limit per day that I would reach?  If so, should I untweet some of these posts to stay under the limit?
Maximum limit of Retweets on Twitter
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Depending on how many tweets you retweet and send then, yes.You are limited to sending 1,000 updates per day broken down into semi-hourly intervals.  If you hit your account update limit, you will have to wait until you have passed the limit-period before you can send further updates.  Retweets are classed as an update.You would also be limited by the API Rate Limits - currently 150 unauthenticated API calls and 350 authenticated API calls.Other Account Limits are as follows:Direct Messages: 250 per day.Updates: 1,000 per day. The daily update limit is further broken down into smaller limits for semi-hourly intervals. Retweets are counted as updates.Changes to Account Email: 4 per hour.Following (daily): Please note that this is a technical account limit only, and there are additional rules prohibiting aggressive following behavior. You can find detailed page describing following limits and prohibited behavior on the Follow Limits and Best Practices Page. The technical follow limit is 1,000 per day.Following (account-based): Once an account is following 2,000 other users, additional follow attempts are limited by account-specific ratios. The Follow Limits and Best Practices Page has more information.Further information on Account limits (DM's, Updates, Following etc) can be found here