After the introduction of the Euro, all coins were counted in standard sized cups which also fit in the cashiers trays so no swapping needed, the error rate reduced to near zero (at counting, difference between amount on bag and what the bank told us was in it). Also, the machine was 500 grams instead of half a small room.
The same was applied to bank notes, as they also have a standard weight due to standerdized size and production method. This reduced the error rate even further as counting is difficult as it turns out if you want to do it at scale. It also made the task way faster. Theoretically the machine could count the notes in one go, but it mostly reported "error check notes" messages if you did that. Things like thick tape (for repair when the bank note was damaged) was enough to throw it off in some cases.
Those were interesting times, with people buying a 25ct item with a 250 note to not go to the bank to exchange old for new currency. (Fyi, you do not have to legally accept that as the due dilligence needed with high notes would outweigh the cost of the item).
Other anecdote: Also a lot of 50 euro fake notes showed up within months after introduction, easilly cought as they lit up like a freshly washed white shirt under UV light.