Rarely is all genealogical information consistent. This is one of the reasons that most genealogical software programs allow for multiple dates of birth, multiple places of birth, etc. This way one can accurately record what each record indicates. It is up to the researcher to determine which location or date is most accurate. This largely is dependent upon the perceived accuracy of the individual sources, etc. Then one can choose the "preferred" date or location. It is always important to include your reasoning as to WHY that date or location was chosen.
Another way to analyze conflicting information is to create a discrepancy chart, listing each different date or place and where that information was obtained. I wrote an article some time ago on using these charts. Unfortunately, I am no closer to learning about great-grandma's parents than when the article was written several years ago.