Single quotes will be your friend: (also notice the difference with the syntax highlighting - the string is in all red, not red and blue - red and blue means you have a problem)
$MovieArray[$m] == '<table width="100%" border="0" cellspacing="0" cellpadding="0">'
But this alone probably won't solve your problem. If and only if that table tag is on its own line, then you will probably need to do trim() on $MovieArray[$m] to make sure there's no dangling carriage returns. So you'd have:
trim($MovieArray[$m]) == '<table width="100%" border="0" cellspacing="0" cellpadding="0">'
Again, this assumes the table tag is put on its own line. If it isn't, then you'll want to look into [man]preg_match[/man].