Hi man, You've nailed the part starting from 0:37 - well done.
The rest of the lesson still suffers from;
Inconsistent muting. The 3 notes at the beginning don't stand out like they should. The only way to deal with this is to make sure you're picking them cleanly and positively.. and make sure the left hand is co-ordinated with it.
You have a tendency to miss off notes at the end of a phrase (like the beginning) or chords at the end of a riff (like the A#5 on the 'Master of Puppets' style verses. It looks like your hand is covering the areas but the notes are not sounding. It could be because you're already moving your left hand away before you've properly picked it ? It's worth looking at closely to try and diagnose the issue.
I'm not sure if's the tone you're using but there's an overall scratchy sound to your riffing. It sounds more 'garage band' than hard rock. I can't say for sure without being in the same room as you so try to work on your palm muting still.. I notice you curve your hand upwards when muting the low E, leaving the strings underneath free to ring out. This may be happening during other parts as well ?? I dunno, you have to be the judge by having a closer look