I think that you belong at a small hospital or in a different type of specialty. People are often given an extra week on orientation but it does not sound like you were ready to safely work independently yet if you were making these small but significant errors and even worse, someone else had to catch them. Giving a patient twice the order dose of medication is a significant issue...it isn't just about splitting a pill. Do you not have access to Micromedex on your Emar because that is a fast way to look if a med can be cut, crushed, or a capsule can be opened. (I disagree with idea that they score meds that can't be cut though...but you should always know your medication before giving it...what is is, what it is used for IN THAT PATIENT, and if you are dealing with an appropriate dose - which means you will be looking up a lot of meds very quickly when you are still learning what it standard on your unit). I verbally tell my patient what I am putting in their pill cup before I even open the wrapper so they can tell me if they don't want it or don't believe it is an appropriate med or dose. I also immediately split the pill at that time and throw away the extra so I don't loose track of what it is).
The labeling of the IV bag immediately may not be as big of an issue but it is a huge concern of JACHO and accreditation issues, so that may have been an issue for them. Or it may just have been a concern that you were not noticing the multitude of small details that are involved in quality patient care.
The problem with not being fully ready when you go off orientation is that you are expected to be able to carry a full patient load independently...and give quality care plus recognize when you need to get advice. I am relatively new to the postpartum nursing side (I am shared by the gyn/med/surg unit) but I have noticed that as the newbie who doesn't have friends on the unit that I often have the most couplets before anyone else. Multiple times I have had to care for 5 couplets which is critical staffing levels on that unit ... and I have to give quality safe care anyway...my new moms and newborns are depending on it. On one of these nights I was caring for a new c-section mother with q2 hr checks for mom, a Finnigan baby with q4 hr checks (respiratory rate funny enough I had to call in the NICU resident to come assess the baby), a 1st time mother who did not speak English as her first and primary language, a baby who could not get his blood sugars stable and the mom was having building a nursing relationship with the baby, and all the mothers needed assistance and teaching with breast feeding. And the whole time doing the normal baby vital signs for babies, full assessments for both, teaching baby care, doing scheduled activities such as Algo, CCHD, weights, TcB, etc. Unfortunately, in a big hospital they don't have time to let you use training wheels when you leave orientation. I am kind of disappointed in the whole orientation process at my huge teach hospital because between the two units I am now qualified to work on, I never had the same preceptor more than twice. It was a huge teach yourself project and I spent a lot of time at home looking up what I didn't know or revisiting my personal organizational plan. I was vocal about my disappointment concerning my orientation and since I had already established myself as a good nurse on the gyn side, I think I was heard because they have since instituted multiple new policies concerning having a more planned and better precepted process.
I do not have any reason to question your ability as a nurse but it sounds like you are not a good fit for a large hospital. I think they were simply letting you know you were not a good fit for this unit the way it is run. Know that in a busy hospital you have to learn fast and perform fast. It isn't personal. And trust me, I went home in tears as many shifts as I didn't because it was hard and exhausting. I spent a lot of time at home looking up policies and things I didn't understand. Post-partum nursing is primarily about schedules and doing things on time even when multiple tasks on different babies are due at the same time, recognizing when a baby or mother is out of the range of "normal", and recognizing when a patient needs teaching and being able to give it with the attention of someone only caring for one couplet. On the gyn/med/surg floor my shift is guided by the patients who are the most sick and need the most care...on the postpartum side, it is driven by a tight schedule of tasks that are dependent of the type of delivery and the age of the babies under my care.
Good luck at your next position. Don't let this one experience steal your confidence. Learn what you can from it and find the unit or specialty that is a better fit. Sometimes life's lessons are about finding out where we don't belong.