It's a bad idea but not because of the reasons you list...
You can dispute a charge and get it reversed, that has nothing to do with whether it has been paid or not.
I wouldn't put a credit card payment on auto payment for a different reason - manually making a payment forces me to see the statement for fraudulent charges.
Imagine someone made a fraudulent purchase using your card and the amount was automatically taken away from your account - your bank balance won't be what you think it should be!
money.stackexchange.com/users/1472/MoneyCone
I've been doing this for years, and haven't had a problem (yet).
Since I pay of the entire balance every month, this ensures that I never have to pay interest because I forgot to send in a payment.
As MoneyCone said, it does require discipline on your part to check your statement each month, prior to the autopay.
Remember, that even with autopay, you can override it for particular statements.
So if there is a fraudulent charge, you can dispute it with the credit card company, and manually pay the card whatever amount you want.
The one thing I do worry about is the credit card making an error and withdrawing more than they should.
This is why I have the autopay tied to my local credit union account, which I only keep enough to pay the credit card bills and the occasional paper check, limiting the damage.
Most of my money are in an ING account, where I use online billpay to take care of the rest of my expenses.
money.stackexchange.com/users/1119/KeithB
Whether this is a good idea or not really depends on how active you are with your money management or how lazy you are about it.
If you are careful with your credit card spending, and always keep within your budget, automatic payment can reduce the time you need to spend managing your credit card account and paying bills.
If you occasionally splurge and need to keep a balance on your credit card (usually a very expensive form of credit) then paying off in full could lead to more money being taken from your current/checking account than you might expect, which could cause other debits to be refused.
However, depending on where you are located, you may have another option.
In the UK, most banks offer the option to pay off the minimum amount automatically by direct debit , rather than paying off the full amount.
For instance: You must pay us £5 or 2.5%,
whichever is higher, of your statement balance, or if less than £5, your statement balance.
Paying at least this portion automatically can be very useful if your credit card company charge you a late payment fee.
E.g.: Default charges, Late payment, £12 In combination with a standing order , it can also make budgeting easier.
You guarantee to pay off the minimum charges every month using the minimum direct debit, and then pay off an affordable amount every month to cover interest and reducing your principal debt using the standing order.
This gives you finer control, but also ensures that you are never stung with late payment charges.
money.stackexchange.com/users/3398/Mark Booth
I used to live on a debit card, but switched over a year ago for the rewards.
I've been doing this for a while.
Works fine as long as you have the discipline to track all the expenses.
The standard ACH precautions apply: the company you let do this can be crazy hard to stop.
But I figure it's worse to incur the penalty fees and interest because I was sick/busy/traveling, as every dollar I spend on my CC
I intend to pay.
While it's easy to set up autopay and never actually look at your spending, it's still dangerous to your wealth.
So I set up an easy system with GNUCash that constructs every transaction I anticipate 1 billing cycle out, and I record a transaction that pays the whole balance off, and when I get the bill adjust downwards to match the actual payment (some transactions get two months of grace period).
If it looks like I don't have the cash to cover the autopay for some reason, I've got time to re-arrange things before the four horsemen of the banking apocalypse arrive.
It also makes it dead simple to reconcile the credit card with what I've got planned: most transactions match up with an existing transaction so any unexpected charges will stand out in yellow as unmatched and uncategorized.
money.stackexchange.com/users/2410/jldugger
I only have 1 credit card that I use and make sure that they money in the bank is always higher than the card limit so having auto-pay means I don't have to worry about it.
As others have mentioned, it doesn't affect your ability to dispute fraudulent charges, so as long as you aren't concerned with not having enough in the bank to make the payment, it makes things a lot simpler.
money.stackexchange.com/users/1683/Davy8
Other answers have talked about fraud.
I've never had sizable fraud on my credit card, but I have had errors.
One in particular was a fat fingered entry by a doctor's office.
I authorized them to bill $540 or so, and they put in a charge for $5400.
It went through just fine (thanks Chase), and then immediately threw my whole account into a mess since that was over my limit.
I had overlimit fees plus the balance over the limit was immediately due.
It was a pain.
At a time like that, I was glad that I didn't have auto payment.
Also, I occasionally have large credit card payments that I need to rearrange money to pay for.
For instance, buying two airline tickets can easily be $1500, and I don't generally have that much in my interest-free checking account.
money.stackexchange.com/users/3931/Scott McIntyre
If you are nervous about that, why not just sign up to have the payments direct debited from your checking account WITHOUT using the credit card.
My house and car payments have been direct debiting for years with no issue whatsoever and it eliminates the risk of messing up your credit by accidentally missing a payment.
Bottom line: Don't bother with using the card as a middle man.
money.stackexchange.com/users/149/JohnFx
I wouldn't worry too much about the charges.
Worst case scenario is if there is fradulent behavior then I've never had issues getting it reversed.
money.stackexchange.com/users/7359/user7359
Many credit card companies offer customers to make their payments via automatic direct debit from their checking accounts. Is this potentially a bad idea for cardholders? One thing that concerns me is that I could lose the right (or at least, the leverage) to have fraudulent charges reversed and merchant disputes resolved.  Are my concerns warranted? Are there any other reasons to not allow credit card companies to automatically debit your checking account?
Auto-pay credit card from checking account: Bad idea?
money.stackexchange.com
<credit-card><checking-account><billing><pre-authorized-payment>
money.stackexchange.com/questions/11339
money.stackexchange.com/users/3048/Tony the Pony
Even with autopay, you can still override it for fraudulent payments. Make the payment manually means you are forced to check the statement every month. Manually making a payment instead of putting a credit card payment on auto payment forces you to check the statement for fraudulent charges, rather than the amount for a fraudulent purchase with your card being automatically debited from your account. Choosing not to set up automatic payments requires discipline to check your statement each month, prior to the autopay. But even with autopay, you can override the payment for particular statements.  
Manually making a payment instead of putting a credit card payment on auto payment forces you to check the statement for fraudulent charges, rather than the amount for a fraudulent purchase with your card being automatically debited from your account. S2: As MoneyCone said, it does require discipline on your part to check your statement each month, prior to the autopay.   S3: Remember, that even with autopay, you can override it for particular statements.  