I'm using this RTC in my project as well.

Yes it does need you to do the error checking as far as setting the clock is concerned. I did a test where I entered the value of 60 into the Seconds register. it kept on counting 61,62,63... until it got to 80, where it rolled over and left 40 behind. After this it continued to work correctly, and rolled over properly at 59, only leaving zero behind as it should.

So to reiterate; an error routine is required to limit the values that someone can enter when setting the clock (and calendar as well), but other than this the DS1307 will take care of itself from a time and date keeping sense.