Aside from the fact that it’s interesting and a little amusing, where would you expect to find deficiencies on this roof.
Due to the steep angles and odd shapes of both protrusions/turret, I would expect that the sealing strips on the shingles would not have bonded. I would suggest these be hand sealed. I would also closely inspect the flashing against the chimney. This is a difficult area to properly flash due to the odd roof angles/curves. Though not visible in this photo, the flashing behind both protrusions could be a potential defect .
Aside from that:
- The top of the dome where the shingles don’t have adequate slope;
- The back side of the turret where it interfaces with the sloped roof and may form a dead valley;
- The interface between the turret and the large chimney on the right where there are odd angles and possibly no/negative slope;
- The flashing installed outside of the stucco on the right side chimney;
- Shingles at the waistline of the dome where the slope is steep and actually past 90°;
- The pointy peak of the dormer that appears to be capped with folded shingle material;
- Metal coping at the top of the chimneys that doesn’t have an edge flange outside the stucco or drip edge;
- Those horrendous faux lintels of stucco like material on the first floor windows (not roof though)…
At the dome and the spire, both of which should have been covered in metal not asphalt shingles.
To go back to the original question.
Anywhere rain snow sleet or any of that stuff can hit it. Look for it there.
First place I would check would be the architect.
The short answer; Everywhere you look.
I wish now I’d knocked on the door and asked them if they’d had any leaks.
Chuck detailed things, BUT Marcel said it short and sweet