Forgetting to set up relationships between the tables. I remember having to clean this up when I first started working at my current employer.
Not doing the correct level of normalization. You want to make sure that data is not duplicated, and that you are splitting data into different as needed. You also need to make sure you are not following normalization too far as that will hurt performance.
Not understanding how a DBMS works under the hood.
You cannot properly drive a stick without understanding how a clutch works. And you cannot understand how to use a Database without understanding that you are really just writing to a file on your hard disk.
Specifically:
Do you know what a Clustered Index is? Did you think about it when you designed your schema?
Do you know how to use indexes properly? How to reuse an index? Do you know what a Covering Index is?
So great, you have indexes. How big is 1 row in your index? How big will the index be when you have a lot of data? Will that fit easily into memory? If it won't it's useless as an index.
Have you ever used EXPLAIN in MySQL? Great. Now be honest with yourself: Did you understand even half of what you saw? No, you probably didn't. Fix that.
Do you understand the Query Cache? Do you know what makes a query un-cachable?
Are you using MyISAM? If you NEED full text search, MyISAM's is crap anyway. Use Sphinx. Then switch to Inno.
I think the biggest mistakes that all developers and DBAs do is believing too much on conventions. What I mean by that is that convention are only guide lines that for most cases will work but not necessarily always. I great example is normalization and foreign keys, I know most people wont like this, but normalization can cause complexity and cause loss of performance as well, so if there is no reason to move a phone number to a phones table, don't do it. On the foreign keys, they are great for most cases, but if you are trying to create something that can work by it self when needed the foreign key will be a problem in the future, and also you loose performance. Anyways, as I sad rules and conventions are there to guide, and they should always be though of but not necessarily implemented, analysis of each case is what should always be done.