Looks like there is no value saved for the field.
This means your in_array function will fail due to the wrong variable type.
Perhaps you need to also compare the value like so:
<?php
if( get_field('materiale') )
{
if( in_array( 'Materialet er tilgængeligt til download', get_field('materiale') ) )
{
echo '<a href="' . get_field('download') . '" target="_blank" class="readmore">Download PDF →</a>';
}
}
?>
