Portability
Assuming it to be on, or off, affects portability. Use get_magic_quotes_gpc() to check for this, and code accordingly.
Performance
Because not every piece of escaped data is inserted into a database, there is a performance loss for escaping all this data. Simply calling on the escaping functions (like addslashes()) at runtime is more efficient.
Although php.ini-dist enables these directives by default, php.ini-recommended disables it. This recommendation is mainly due to performance reasons.
Inconvenience
Because not all data needs escaping, it's often annoying to see escaped data where it shouldn't be. For example, emailing from a form, and seeing a bunch of \' within the email. To fix, this may require excessive use of stripslashes().