Make sure you position your finger as close as possible to the superior metal fret, this will ensure better sound quality and help you get rid of that buzzing noise that's been driving you crazy.

Disclaimer: Make sure you apply just enough pressure, squeezing too mush or too little will cause string buzzing or bad sounding notes respectively.

Check out min @4:08 for a demonstration.

Bonus tip: Use the tip of your finger to fret any given note!

What you want to be doing is alternating the picking direction so going:
-Down Up, Down Up.

Instead of:
-Down Down Down Down.

This will help you gain speed and reduce the risk of accidentally hitting unwanted strings creating unwanted noise.

Check out min @4:40 for a demonstration.

What you want to do instead is do smaller arcs without moving too far away from the guitar when playing.

Smaller movements = Less chances to make unwanted noise + More Speed

Check out min @6:03 for a demonstration.

-Stop playing
-Full focus on fretting the chord correctly
-Continue playing.

And this completely kills the flow of the song.

Ideally you want to practice faster chord switches, and get better at strumming along any chord progression with ease.

But for the time being here is a tip for your next jam session, most people are tone deaf but have a very good sense of rhythm.

Meaning if you play any wrong note, they probably won't notice but if you break rhythm most people will realize something isn't right.

So all you have to do is keep the flow going, you could just mute the strings, keeping the groove going and skip that hard chord all together.

Check out min @8:29 for a demonstration.