Continuity mistake: Before Edward is looking at the family pictures you can see some scars on his face are open, when the camera focuses back on him the scars are closed.

Edward Scissorhands (1990)
Ending / spoiler
Directed by: Tim Burton
Starring: Anthony Michael Hall, Dianne Wiest, Johnny Depp, Winona Ryder
Edward kills Jim after Edward sees him hurt Kim. He and Kim know that if he goes back to Suburbia they'll kill him, so they kiss, she tells him she loves him, and she leaves him in his mansion. They never see each other again. It turns out the old woman narrating the story is Kim, telling the story of Edward to her granddaughter, and that he is the reason that snow falls from the sky from then on, because he's making ice sculptures.
Catwoman007
Trivia: This role of Inventor played by Vincent Price would be his very last in a motion picture. Shortly after narrating and starring in a couple of television shows and a voice-over for an animated film, he passed away in 1993.
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Answer: The blood came from another wound on Jim's body. Edward did cut him on his arm and he does fall back onto Kim so she could have gotten some blood onto her dress that way.