How do I fix these horrid vertices? They're on the rim of the cup and very terrifying
These vertices on the rim of the cup are terrible. How do I fix this? or should I start over? What went wrong? Please let me know if the link is restricting access.

I had a quick look at the cup, the geometry is quite messed up (asymmetry, overlapping, additional loops you don’t need). I’d start over, maybe keep the handle.

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failed to download network error ?

You made this from the coffee cup parts of Blender Guru’s 2019 Donut tutorial? I just rewatched those, I have no idea how you got this mess from that (although you have Proportional Editing on, that probably caused some of your problems). You’ve even got a single vertex pulled over a meter on X. And I disagree with LordoftheFleas about the handle, in Front Orthographic view it’s clearly bent.

I don’t know a way to fix this that isn’t far more work than just making it again, sorry.

I noticed that^^, just thought it may have been a stylistic choice.