Handling NULL fields is an issue with any database. Since an undef produces zero-length output, it cannot be sent to the database (the SQL statement would look like 'COLUMN=,OTHER=' which is not what the DB wants).
Null fields can be handled in a simple statement: $nullable = 'NULL' unless $nullable;
This will eliminate the nasty error when you're setting DB columns to undefs...
You could also use "COLUMN='$nullable'" for strings, but that would store zero length string in the database instead of NULL making queries much more comples (you'll need to check agains both empty strings and NULLs for unset values).

Strings can be handled the same way by adding the quotion marks to the string variable intead of the SQL insert (enabling NULL fields to be inserted):
$string_var = "'$string_var'" if $string_var;

Of course, if the string can be null, the quotation marks need to be added before the string is verified against undef or you'll have columns with 'NULL' values instead of NULL.

To make things simple, create a function which does validation. If you need to stop on missing fields, use the code suggested by Russ.