Forgetting to check the appropriate checkboxes. 
Incompletions. 
Figures that do not add up.
Writing lengthy, pretentious clauses like one who fancies themself an attorney. 

Bryan,

Not learning the paperwork thoroughly, and understanding it to the point you could explain it to a 3  year old.

Not having someone double check your work!  A

Watch your commas and decimal points Bryan Gardner .

all paperwork should be reviewed before being submitted, when an agent is NEW.... there MUST be a trainer/mentor.... paperwork is an easy word to say...it's a contract!!! a legal document when fully executed.

This will likely vary by state. If you are concerned about avoiding mistakes(and good for you for being aware-discuss with your broker or office manager). Paperwork control and knowledge is quite important. 

You forget important stuff on the listing agreement. Highlight all those parts that need to be filled out for homes & different ones for condos.

Who does the earnest money get made out to Bryan?

How to write a sales contract. Highlight those parts that would need to be filled in the majority of the time.

• Lack of a full understanding of each and every contractual clause.
• Missing initials
• Using the wrong form (yes, I've seen that many times!)
• Not writing N/A in blank spaces
• Agent-written addenda (not permitted here in NC or SC unless written by an attorney)
• Full description of personal items to remain in the home.

Most common?  Poorly written Addendums and not adhering to deadlines.

Usually, the most severe mistake is not accounting for funds as required.

 Unauthorized Practice of Law, via agents writing in additional clauses.

I am always happy to know that our broker is checking my loops when I turn them in to make sure nothing is missed.

Generally speaking, errors & ommissions- exactly what we have E&O Insurance for.  Specifically, math errors- sometimes the Money Down/Mortgage/Deposit don't = the Offer Price. I've seen illegible contracts, mispellings and vague items that could be an issue later. 

Not having someone else review it, like your broker. Rushing and proof reading

Mistakes are made when the newb really doesn't know what his customer is signing. So my advise is to read the contract and fill it out with the customer. 

Usually the math on the purchase contract.  Putting a number in the wrong field, missing a checkbox or having one checked that didn't need to be.  Missing an initial (page 8 of our purchase agreement is notorious for this since it has three spots for initials, two of which are buried).

The forms require a blank filled in or a box checked. Users have to know why and explain it to others....

Not checkiing your work

Can we start with how we structure a question?

math.

Not knowing what you are doing and failing to ask you broker for assistance when you are in over your head.

There are lots of mistakes but missing initials of forgetting to check a box are two that come to mind.

Illegible handwriting, avoid this. Use typed forms. 

Complete the check boxes completely, review them with someone to ensure nothing was missed, or you could be in trouble. 

Ambiguous addendum drafted by the other side.  We have a blank form my office refers to as the addendum of death. It's where any agent will be exposed and liable to be sued if they don't clearly cover all the basis in a concise way.  Who, what, when, where and what if.  I don't care about why. 

Not reading them and understanding them.

Grammar is a biggie when they can't understand your writing.

Not learning proper procedure and developing systems!

Candice A. Donofrio nailed this one!

Basically not knowing what one is doing.

Failure to get everything signed/initialed !

Proofread

Incomplete and with incorrect information.

Bryan Gardner - I do not want to add to the list... lol!

Check, recheck, let someone else to check it for you.

Many mentioned here in the comments I'd say. Usually as a result of lack of experience.

that's why broker review is required in my state to prevent mistakes.

Always have someone to check your paperwork: broker or your mentor, or at least another agent.

I hope you find the best answer on your guestion. 

A lot great answers are here, Good luck.

I see many very poorly written contracts, missing information, etc.

Add an extra "o".  

Not proofreading, for starters...

Expressing yourself clearly using proper grammar when you write something. One small error in the wording of a clause could have detrimental effects.  A good example is your question... :)