Is it okay to ignore the error notices I get on a Drupal site?
Between the two errors, the first is more worrying.

As variable_set() passes the variables value it receives to serialize(), if unserialize() is not able to understand the saved data, it means the database content is probably corrupted. variable_initialize() calls unserialize() using the following code.

  // Proceed with variable rebuild.
  $variables = array_map('unserialize', db_query('SELECT name, value FROM {variable}')-&gt;fetchAllKeyed());
  cache_set('variables', $variables, 'cache_bootstrap');
  lock_release($name);


The second error says the code is using a feature that is deprecated, which means that in future PHP versions the code could not work anymore, but in the actual PHP version is still working.