Can I detect and handle MySQL Warnings with PHP?

For warnings to be "flagged" to PHP natively would require changes to the mysql/mysqli driver, which is obviously beyond the scope of this question. Instead you're going to have to basically check every query you make on the database for warnings:

$warningCountResult = mysql_query("SELECT @@warning_count");
if ($warningCountResult) {
    $warningCount = mysql_fetch_row($warningCountResult );
    if ($warningCount[0] > 0) {
        //Have warnings
        $warningDetailResult = mysql_query("SHOW WARNINGS");
        if ($warningDetailResult ) {
            while ($warning = mysql_fetch_assoc($warningDetailResult) {
                //Process it
            }
        }
    }//Else no warnings
}

Obviously this is going to be hideously expensive to apply en-mass, so you might need to carefully think about when and how warnings may arise (which may lead you to refactor to eliminate them).

For reference, MySQL SHOW WARNINGS

Of course, you could dispense with the initial query for the SELECT @@warning_count, which would save you a query per execution, but I included it for pedantic completeness.

First, you should turn warnings off so that your visitors don't see your MySQL errors. Second, when you call mysql_query(), you should check to see if it returned false. If it did, call mysql_errno() to find out what went wrong. Match the number returned to the error codes on this page.

It looks like this is the error number you're looking for:

Error: 1169 SQLSTATE: 23000 (ER_DUP_UNIQUE)

Message: Can't write, because of unique constraint, to table '%s'