starting new job at bank?

You've not described anything worrisome.

You should at least have the month and year right on a CV but the debt you have might be more crucial. Financial institutions regard a high debt as an idicator that an employee might be more tempted to steal or embezzle than if they had low or no debt. Even with debt, if your credit rating is good then you should be okay.

Of course, if they don't hire you it could be for an entirely dif reason, too. Good luck, they may very well hire you if you're called back and make a good impression in the interview.

A background check could take a week of so, depending on who they hire to do it and how thorough they are. If you do not hear anything within a week, give them a followup call.

You're probably OK, but here's a few points to consider:

1. There's no reason for dates on your CV to be inaccurate. You don't need to list employment down to the day, but list in MM/YYYY format.
2. Debt is OK, but they're probably more interested in credit score, and the likelihood that you are over leveraged.

After a week or so, I'd probably send a quick email to the hiring manager asking about the status of your application.

I don't think you have any thing to worry about. Some people are a bit off when it comes to remembering when they're hired or when they left a job.
Work hard and do your what you're supposed to do to get past your probation / trial period.