Varies from agency to agency. If this position is in a large financial institution, they tend to use some of the better agencies and the checks are fairly extensive. I would say though, that the odd ommission, date inaccuracy etc on a CV or the like is not likely to convince an employer to revoke a job offer. If they did, the banks would struggle to employ anyone. They are already fairly bad at recruiting in my experience.
The better agencies would check these such things:
details on your CV (employment history, qualifications, nationality etc)
addresses (current and past)
criminal record, civil judgements
credit file, bankruptcy
public profile/media exposure
As I said, it varies. Good luck.