That is certainly non-typical framing. The joists laid flat are on the same spacing as the joists oriented vertically (albeit with a smaller span). I don't see any joist hangers at the right end of these joists. And the beam supporting these joists (left side of photo) also appears to have a significant chunk removed from the bottom edge (again, possibly for headroom).

It is not your call as a home inspector to say the deck is or is not structurally sound as built. I would recommend that you note the non-standard framing practices and the notched beam and recommend the deck be inspected by a qualified professional.

By the way, check out Brian's link to an article on "May Is Deck Safety Month".

__________________
"Baseball is like church. Many attend but few understand." Leo Durocher
Bruce Breedlove
www.avaloninspection.com