Where your tape edge is close/very close to the underlying drywall joint, I would expect to see cracked joints n the future if left alone. I would wet it, let the water soak into things, and then carefully peel the tape off, clean the excess mud off and start over. I'm also not fond of paper tape (I tend to push too hard and squeeze too much joint compound out), so I use mesh tape instead.

So would you say the first two pictures need to be re-taped, but the third (where there is more room above the join) is ok?

If the third one should be re-taped, I'm going to have to do a lot of re-taping, since that's most of the room :( . But where it's as bad as the first two pictures is just one little section.

Here is a link to some videos to get you started.

https://www.youtube.com/playlist?list=PL_Aetb7e8ejxJi5m7iZBY91M-t4WLVEv1

This is your first image, and I'd redo any tape that looks like this. Also see the circled spot. Tape probably not stuck there. The tape looks dry. What type of mud are you using, and are you thinning it any (you probably should be).

Thanks for the response PPF.! I have been using this video for reference: https://youtu.be/naBal346_9c?si=Yh_H6DeuS1rC0Jjh

I am using premixed joint compound, and yes I am thinning it out with water and using a mixer drill attachment to mix it (basically following instructions from the video I posted above). I did notice that spot as well - it is not an air bubble, it is hard if you press it. I think it's a small chunk of drywall that chipped off close to the butt joint, probably caused by me puting a screw close to the edge. I was going to just take a razorblade and cut the little bump out.

I can redo that piece, but what about the third picture where it isn't quite as bad? I don't have the experience to know how bad is bad enough that I need to redo it, and that would determine how much of the room I need to re-tape. If the third picture is still bad enough, I probably need to redo almost the whole room.

Just watched the first 14 minutes of your reference video. Suggest you watch it a couple more times. Focus on keeping things neat and leaving a smooth finish free of ridges. Nothing wrong with using a 6" knife to wipe the joint down as your final pass. Try for a uniform coating under and over the tape.

I'd say picture 3 might be OK, but anywhere you have less than 5/8" of tape (3/4" is better) on one side of the seam, it's a do over.

PPF. - any suggestions for how I go about redoing the tape? Am I able to just peel the tape of (afer wetting it), or will I have to sand the mud off?

Damp sponge (dont soak it), and the mud will smooth out nicely. It seems, like you are using paper tape, and not getting the mud under it evenly for the tape. You may want to use fiberglass type tape that sticks by itself, and mud goes on afterwards. Its not hard to center the tape with the seam , and get nice straight tape lines. Dont put any mud on any of it, until you have taped every single seam, on the new drywall, and then mud all the areas over the screws. Hopefully, you havent broken the paper on the drywall with the screws. They should be recessed, but, not break the paper itself. Hopefully it will all go well for you.