The exec function callback has error, stdout and stderr arguments passed to it. See if they can help you diagnose the problem by spitting them out to the console:
exec('~/./play.sh /media/external/' + req.params.movie,
function (error, stdout, stderr) {
console.log('stdout: ' + stdout);
console.log('stderr: ' + stderr);
if (error !== null) {
console.log('exec error: ' + error);
}
});