When Simon Moore comes up from the basement, he leaves the basement door wide open. When McGarrett and Danno get to the door, the door is closed. When McGarrett throws the stun grenade into the basement, the door is partially open.
This episode is an immediate continuation of the Season 5 season finale, picking up immediately after the wedding. Kono's hair was tied up for the wedding in the season finale but is down when they are introduced as Mr. and Mrs. Noshimuri.
At least one of the pirates had an 18th century type pistol in 1884 (late 19th century). The leader had a revolver, which had been in production at that point for decades, so the remainder of the crew would have been similarly armed.
The pirate raid was in 1884. Washburn was shown as a young man (same actor), maybe a 20-something. In 1975, he is 104 years old and interviewed. 1975-104=1871. That would have made him about 13 at the time of the raid. His true age was eventually figured out but should have been obvious to the police right away.
When the team are figuring out that the frame of the painting holds the key to finding the treasure, Jerry says he needs a picture that matches the painting in size. He then uses the back of the frame to locate "x marks the spot". However, the picture is not the reverse of the painting as it would be viewed as from the back of the frame. Therefore the location of the intersecting lines would be way off.