If you integrate acceleration over time to get velocity you will also be integrating any offset or other error such as rounding or precision. Also remember that the readings you are getting are instantaneous values for a continuous process. The value represents the current acceleration, not the average acceleration sine the last reading so if the acceleration is changing, using the current value as the average for the last time period will introduce errors.
Of course if the accelerometer is not in a fixed orientation relative to the local gravity you can't tell if the acceleration you are reading is due to change in velocity or due to gravity.