I don't know if you're just curious or considering entering the business. If it's the latter, I'd suggest reading "Your Successful Real Estate Career" by Kenneth Edwards. It is a really good overview about starting out in this business.
My biggest dislikes in this business are all related to Realtor behaviors actually. There are a few basic areas in which I'm referring. One is the everyday on the street Realtor behavior and the other is the behavior of our representative Associations (i.e. the National Association of Realtors, and local Realtor Boards and Associations).
There are many Realtors practicing who do not adhere to the standards of behavior and practice that the Realtor community expects (and that consumers should expect). Michael from Hamburg NY gives a great example of that in his answer. There are many things that should ALWAYS occur in any transaction (like pre-qualifying buyers over the phone and having buyers sign Buyer's Brokerage Agreements- which virtually no agents do in Illinois at least). But because of the sloppy and common past practices of these many Realtors consumers do not know or realize when they are being served well or under-served. In some cases adhering to the true standards of practice in real estate brokerage can put you as a Realtor at a competitive disadvantage against other Realtors who are not "demanding" the same things from their consumers or clients.
The second edge of that particular sword however is that if you are the agent that tends to do things by the book, you often have much more happy and well-informed clients who understand the value that you bring to transactions (as well as much less legal liability).
Our local and national associations of Realtors could and should do a much better job of setting expectations for and educating consumers about what they should expect from their Realtor. Susan is very right about educating consumers, but I think that the associations that I referred to earlier are in a much better position to do that than we as individual practitioners are. Although I can acknowledge that local practices may make it difficult to have a uniform national message about what clients should expect, the local and regional associations should be able to pick up the proverbial ball a bit and run with it with respect to local variances in real estate practice.
The only other on the street practice that I sometimes have a hard time with is people who say or ask things that are legally actionable (meaning someone in the room speaking of listening could get sued over them). This most often revolves around people making statements about someone's ethnicity, race, national origin or sexual orientation. Acknowledging what was said and dealing with it in a positive way that does not completely obliterate the relationship (either with the client or another agent)- those can be trying conversations.
The rest of the real estate business can be handled with good humor including clients who are abusive, clients who conveniently forget things that are problematic for them (or cost them money) and delivering "bad" news to clients. There is nothing to fear in real estate except fear itself (and occasionally other Realtors).
Broker Associate, Sudler Sotheby's International Realty