There are numerous things design wise that are wrong with this class.
Firstly, it is tightly coupled with the mysql extension. Instead, you should be passing a database object (implementing an interface that this class recognises) into this object.
Secondly, there are several places in the class that output error messages within this class. Classes should not output anything (unless that is what they are designed to do) but instead throw exceptions or have methods simply return false.
Other than that, it's a pretty good start. I would however recommend using the more common php5 syntax instead of the php4 syntax.