Heck, all of those sound like typical new nurse mistakes. Heck, most of them we've all done! I don't do it a lot, but I have thrown out a med still before scanning it when I'm tired. It happens! For me mistakes are just a part of how you learn. I'll give you an example. Forgetting to open the clamp on your secondary IV tubing. Ugh! Done it more than once when I first started (and have seen experienced nurses do it too). It happens. Now I am almost OCD about checking those clamps are open. Nothing more annoying than realizing you accidentally ran your primary bag at 300 ml/hr for 20 minutes. Oops.
Not too long ago I was floated to another floor and I swear to God I counted the narcotic drawer wrong 3 times! I wasn't expecting this med to be a controlled substance and it popped open like a regular drawer would so I had already had meds in my hand and then it asked me to count. Well guess what I still had the pills that I pulled in my hand and was not counting them with the pills in the drawer. Oops. I did figure out what I did wrong when finally on the 3rd time when a discrepancy was opened that I still had the med I pulled in my hand.
The problem with being new is instead of doing this stuff occasionally you do it often. You'll get there. Next job you watch you'll be the nurse that's getting it when the other one isn't. Don't beat your up, but don't discount the advice you're being given. You probably are the slow nurse right now, better to be the slow nurse than the stupid nurse. You haven't said anything that makes me think you don't have clinical knowledge. Don't sweat it. And if you have to get another job, you won't be the first nurse that it's happened to. I went through 2 jobs in 3 months when I first started. It sucked. I felt like a moron. It gets better! Hang in there.