Personally, I tend to do two things differently:

• First, I select a full list of primary keys and put it in a hash. Before I try to do an insert, I check to see if the primary key for that record exists in the hash. If it does, I do an update instead of an insert. If the primary key isn't in the hash, then I do an insert, and add it to the hash if the insert was successful. This seems to be a little cleaner and (potentially) halves my number of SQL executions.
• Second, I tend to use the RaiseError option in my database connection so that my program doesn't die when DBI encounters an error. I examine $DBI::errstr to specifically identify the nature of the error (in Oracle, you get error codes) so that I cover my bases for the unexpected. There's no sense in attempting an update if the table doesn't exist or your SQL is malformed. I'm not a MySQL guy, but the use of eval and $@ seems less than precise -- you might react to what you think is a duplicate insert error but is really something much more severe.

Update: As noted by kyle above, however, if this code is executed by multiple users/processes, you could end up with a race condition, such that your inserts might still fail because some other guy just added that record since the time that you selected all the primary keys.