I will repeat what the others have told you. Don't worry about the sail and sign card. Back it with a CREDIT card (not a debit card) and you will be fine. Yes, you can back your card with cash if you want but then you are carrying cash around.. not worth the risk in my book. If you have 2 credit cards, bring a second to use off ship and leave the sign and sail one on board. If your credit card is lost or stolen in port, your can cancel it and not have to deal with changing your on board account setup.
Yes, we check our balance as we go. Its easy to do, you can do it from the TV in your cabin (or ask the pursers desk to print out your account.) My wife collects all the receipts and then checks them against the account. If you find something that does not belong or got double charged, take your receipt to the pursers desk and they will fix it for you. It does happen, but not as often as the posts you are reading make it seem. Remember, people only tend to post a negative experience. Compare the number of bad S&S posts you see with the 10s of thousands of passengers that sail on Carnival in a given week... that will put it in perspective.
If you are traveling with kids, you should consider not giving their cards purchasing privileges. That way they can't charge tokens in the arcade or be buying sodas unknowingly. If you want to give them credits to play with you can go the arcade and "load" credits on their card using yours in the machine there. And if you want to get them soda cards you charge that on your card anyway. So they really don't need charging privileges...
Have a great cruise and don't stress about this, there really isn't anything to stress about. (oh and the checking the bill before the last night is good advice. The line is very long the last night, so check it early morning on the day before disembarkation day or even the night before that)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013