Does LIGO have a blind spot? If I understand the principle of operation of operation of LIGO, it detects relative distortions of the two perpendicular arms. So if both arms are distorted the same way, nothing would be spotted.

In particular, any wave coming in the direction 45 degrees between the arms (both ways), or from above or from below - or generally any direction in the symmetry plane 45 degrees to the arms - would be completely invisible, and anything close to it would be very muted as the relative distortion would be minimal.

Is that correct?
This paper should tell you all you need to know about how LIGO observes and localizes gravitational waves, and in particular its blind spots. The map below is taken from the paper and shows the observability of the system when in the  HLV configuration (Hanford-LIGO, Livingston-LIGO &amp; Virgo). To triangulate a source by definition you need at least 3 measurements so that is why Virgo is included, although the two LIGO detectors can make very broad estimates for source localisation on their own (GW150914 was assigned a 600 square degree error box). 

The (x) denotes a blind spot.