Wrong employment dates on resume?

A month one way or the other probably won't matter, If you said you worked there a year and it was really only five months, it would matter.

Depends what you did in that hole of a year and the way excessive a role you are going for. Often i would say, do not lie however be liberal with the truth and hell you can always say it used to be a typo. In the interim grow to be so just right at your job that they'll not need to sack you in the event that they ever find out. On this case a small lie may just deliver big rewards and what the intellect does understand, cannot hurt it.

Best case scenario is they think it's an honest mistake to be off by just a month and let it slide. Worst case scenario is they think you're careless/don't have attention to detail or even dishonest. Since it's only a month it'd not likely to think you lied since who would bother lying about just one month?

I wouldn't want to take any chances though. Correct your resume now that you know and when you walk into an interview give them the updated one with apologies.

Depends on the job. Some will not check dates at all. Some will be very picky.