I am currently living in Montana, and I received one year of probation for criminal mischeif and criminal trespass, if I were just to up and leave state without telling anyone, would I be allright as long as I didn't return, or would there be a nation wide warrant for me no matter what state I went into?

No, they will put out a warrant for your arrest. Once you are caught you will most likely spend the next year in jail.

The warrants are all nation wide, so you will not be able to get a job where they do a background check,

Will not be able to renew your drivers license, which means you can't get tags in some states without a valid drivers license.

And when found, they would most likely haul you back.

So even if you moved so far away, that they would detain you but maybe not send you back, you could not drive a car, could not get a better job and would even have trouble renting many apartments