Posting link-type updates. Facebook gives the least exposure to updates that feature a link 'card'. Your update will be seen by more fans if it contains a photo.
Making it all about them. Posting interviews with the CEO, press releases, etc. Facebook pages are a place to involve your fans, give them opportunities to give you feedback, and provide content they'll find valuable / worth sharing.
Putting @mentions at the beginning of the tweet. This is called an @reply, and it's not seen by any of your followers unless they are also following the person you're @replying. If you want it seen by everyone, put a period or other character in front of it. e.g. ".@JayNeely is super handsome!" not "@JayNeely is super handsome!"
Overusing hashtags. It's super spammy and gets your tweets ignored. Most hashtags really don't provide much additional exposure. It's best to only include hashtags when they're in use at an event, when they're part of a trend or twitter chat you want to be part of, or as a 'stamp' to change the tone of your tweet. #forreals
Following more people than are following you. Looks spammy. When you're starting from scratch, get everyone you know off of twitter to follow you on twitter, and follow carefully. Earn follows from @mentions and interacting, not from mass-following in hopes of follow-backs.
Not using twitter search / saved searches. For marketing, it's twitter's most powerful feature.
Not using hashtags. Unlike twitter, hashtags aid instagram discovery quite a bit. Too many can still look spammy, but not using them at all puts you at a disadvantage as far as reach goes.