We measure the effect of small amounts of systematic and random label noise caused by slightly misaligned ground truth labels in a fine grained audio signal labeling task. The task we choose to demonstrate these effects on is also known as framewise polyphonic transcription or note quantized multi-f0 estimation, and transforms a monaural audio signal into a sequence of note indicator labels. It will be shown that even slight misalignments have clearly apparent effects, demonstrating a great sensitivity of convolutional neural networks to label noise. The implications are clear: when using convolutional neural networks for fine grained audio signal labeling tasks, great care has to be taken to ensure that the annotations have precise timing, and are free from systematic or random error as much as possible - even small misalignments will have a noticeable impact.