This is a digital interface, that means if there are transmission errors you will get CRC errors. It does not impact the temperature accuracy.
The pull-up pulls the data-output of the Sensor back to high after it has been driven zero by the sensor data-pin. If the capacitor of the data-wire becomes larger more charge has to be delivered by the pull-up. That means a weak pullup needs more time to charge this capacitor.
In doubt connect an oscilloscope to the data pin and look at the quality of the rising edges.