As many of you know, I have been through literally tons of change of all denominations and I find that pennies and dimes are the most frequently miscounted coins. Dimes first, pennies second. I assume this is due to their somewhat similar size and weight. I have also noticed that typically dimes are the first type of coin to be miscounted when a machine goes out of calibration.
The type of coin counter has a great deal to do with how accurate the count is which is why I bring almost all my dumps to the bank(s) I do. Some machine(s) do terribly with certain coins.
However, since I mainly do bags of coins, I end up dealing with the count being off on 95% of the bags I do, usually just a few cents and not worth the hassle. Some high and some low and more or less they average out. Of all the bags I do, the one that is most frequently wrong is dimes. Unless the bag is off by more than $2-$3 (up or down) I never bother to say anything to my pickup bank and just assume the ups and downs will average out. However, more than that and I inform them that the bag was off. If it was short, I don't expect compensation. If extra, I offer to pay it back (I have gotten an extra $90+ a couple times and just the other day I got an extra $50+ in dimes). So far, I have always been told just keep the extra when it occurs as they assume it balances out with the shortages (which it does). I typically tell them, though, so they can have their machine fixed as customers are being shorted (or overpaid) if the count is wrong and they appreciate my honesty (which I believe helps them to continue selling bags to me).
That is at my pick up bank.
At my dump bank, I use self serve coin machines and I usually cash in dimes first and make sure the total is approximately correct (again I don't complain if a couple dimes were counted as pennies). Once in awhile, I have noticed that a high number of dimes has been counted as pennies. If the amount I feel is sufficiently off (more than $1-$2), I stop print the receipt for the dimes and continue with any other dumping I have to do and get a second receipt for that. When I am done, I mention what happened to the teller and show them the receipts. I have never demanded to be compensated, but have suggested if there is anyway to make this right as I know their machine is miscalibrated and to this point about 90% of the time I have gotten them to pay for the miscount (usually its just a couple of dollars, but once it was about $10-$15).
I have also had a couple occasions at a bank that didn't have a self-serve coin counter and I knew the exact amount I had brought in. Once it was halves, once it was nickels. In the case of the halves, it was only a a couple dollars short and I was still at the teller window so I asked about it and I think the teller got frustrated due to other things going on and that it was at closing time such that she just gave me the benefit of the doubt and added the $2 I said it was off. With the nickels, I realized after I left and was thinking about it that I felt like the count was $10 short on $130 or so in nickels. I called the bank later and spoke to the teller who had helped me. After a little explanation as to why I believed the count was wrong and why I was pretty sure on how much I had brought in, she either reran the bags or waited until they were counted by the armored service. Either way, they validated that the nickels were indeed off by approximately how much I said (plus a little if I remember correctly) and she put that credit into my account.
I know I have been fortunate in getting my money back when the machines don't work as they should, but I have also never demanded compensation for it or been upset and just assumed any offage was part of the game we all play. I personally believe that mentioning you believe the machine is off is not a no-no, but since it is a he-said, she-said kinda deal in which there is no easy way to verify who is right, all you can do is ask if there is something they can do to make it right, but don't press too hard if they say "No" as all you are giong to do is rub people the wrong way for a couple of dollars. If it happens continually, you always have the alternative to let your feet do the talking and bring your business to another bank.
One last note, if you are going to complain when the machine shorted you $2+ counting dimes, do you also tell them when the machine counts gave you $2+ in extras when counting pennies? I would hope so.