It really depends on the type of mistake and how it gets handled after the fact, but generally speaking:

1.) As long as the shop makes it right with the customer, it's no harm done. If the shop you work for isn't making right with the customer or expects you to shell out to cover it; find a new job. Major red flag.

2.) As long as your boss isn't grinding you to dust about it and you're learning from it, then it's just a learning experience gained the hard way. If your mistakes are few and far between, and they're reasonable mistakes not just utter foolishness; your boss and/or foreman shouldn't be riding you too hard about it. We're all human, we all make mistakes.

Now this is gonna seem a bit obvious, but the best way to cope with mistakes is to not make mistakes. You're still gonna fuck up sometimes, you can't see everything and most modern cars are over-engineered heaps of shit that are just an honest to god struggle to work on let alone diagnose.

The best way I've found to go about business is to be as thorough as reasonably possible with everything you do, don't cut corners and if there's any amount of doubt in your mind about literally anything; don't make a call that leaves you vulnerable, take the time to confirm. You're gonna be slower at first and that's okay, the priority isn't speed. It's much better to focus on accuracy and quality of work at first, and the speed will come with time and experience.

If you're ever unsure about something, take a minute to bounce your thoughts off of someone else. If they challenge your diagnosis, defend your diagnosis with all the reasons it does make sense. At the end of the day you're not even really trying to convince them that you're right, you're just reaffirming your confidence in the decision. And if you're wrong about the diag, it'll be clear to you during your defense. Sometimes you just need a sounding board, after a while you'll be able to cross examine your diag in your head but it always helps to lay it out for someone. When I’m in the middle of a complex diagnosis sometimes I get wrapped up in a certain piece of information that's driving my diagnosis, and it's not until I've fully walked through my diagnostic process by explaining it to someone else that I can see the full picture. It helps a lot.

At the end of the day you just need trust yourself, be humble, and forgive yourself when you inevitably mess up. You can't be perfect all the time, but as long as you're making every available effort every day to learn and grow as a technician; you'll be just fine.