When Falcone and Valo attempt to escape Glauren's house when Hellboy is having sex with her, the camera they are using to film the act has a "fish-eye" lens on it. After escaping from the pursuing Hellboy, Valo begins to film Falcone "getting his ass kicked" and the camera no longer has the fish-eye attached. At no point would Valo have had time to remove it.
When Falcon and Valo find the poster for the "Invention of the Future" contest, they are standing next to an early-1990s dark gray Nissan Maxima. In the next shot they are standing alongside a late model gold Ford Crown Victoria/Mercury Grand Marquis, but if you look down the street, you can clearly see the Maxima and the posters from the original spot. By the end of the sequence they are back next to the Maxima.
When Falcone and Valo are getting ready to break into Glauren's house and Falcone is talking to the "Tetris Addict", during a seemingly uninterrupted series of dialog between the characters, the level and amount of tetris blocks changes many times on the TV.
After Ryan leaves the table in the restaurant to use the phone, we see the table again, except Ryan can be seen standing at the back of the room in the reflection from the window though he is still on the phone.
Glauren's clothing changes many times after her dinner date with Ryan. She entered Hellboy's car barefoot holding strappy shoes, wearing a transparent purple top and a black skirt. Next time we see her at a bonfire, she is wearing calf-high boots. When she goes back to her house with Hellboy, she's wearing a gray top, stockings, and calf-high boots.
While Ryan is getting arrested, one shot shows him being turned around to be handcuffed, with his back facing the officer. In the very next shot, he's facing the officer again, and the shot after that has him with his back to the officer again.