
Double Trouble in the Panhandle - S4-E12
Continuity mistake: Angela comes in to say she has found the twins. When she pulls up the website she opens up a pop up showing the twins. The position of the pop up changes between shots. Note the size of the banner under the pop up. (00:03:40)
Double Trouble in the Panhandle - S4-E12
Continuity mistake: In this episode we see Booth bare-chested after the hockey match. However, he has no scars on his chest where he was shot in an earlier episode. (00:03:50)

Continuity mistake: The blood drips on the glass in front of Bones near the end has 2 distinctive lines of blood. In the following shots the blood pattern is different. (00:27:20)

Continuity mistake: Hodgins takes the lid off the fish blender twice when trying to find out what killed the fish. (00:32:00)

Continuity mistake: Hodgins goes from holding the jewellery found in the fish tank with one hand to two hands. (00:34:50)

Continuity mistake: At the end, Parker has blood on his cheek that disappears almost instantly. (00:38:00)

The Princess and the Pear - S4-E15
Continuity mistake: When Hodgins finds the sword the plastic wrap is very wide around the hilt. When he holds the sword up, the plastic is flush with the hilt. (00:20:40)

The Salt in the Wounds - S4-E17
Continuity mistake: When lowering the remains into the tank, Aristoo's grip on the remains changes instantly. (00:11:05)

The Salt in the Wounds - S4-E17
Continuity mistake: When Bones and Angela are talking over lunch, Angela has her hand up by her head on one shot and then reaching out and holding the salt in the next. (00:20:40)

The Salt in the Wounds - S4-E17
Continuity mistake: When Sweets is in the chiropractor's office, the doctor is pulling at Sweets' arms across his chest in one shot but in the next his arms are by his side. (00:35:10)

The Salt in the Wounds - S4-E17
Continuity mistake: The way Booth's hands are clasped when talking to Clint at the end in the diner changes between shots. (00:39:00)

The Doctor in the Den - S4-E18
Continuity mistake: When Angela first walks onto the platform at the start and starts flirting with Clark, the way she holds her folder changes between shots. (00:03:30)

The Doctor in the Den - S4-E18
Continuity mistake: When Booth is questioning Brandon for the first time, Booth and Brandon's positions in the interview room are different to the live feed behind the glass. (00:16:40)

The Doctor in the Den - S4-E18
Continuity mistake: When Hodgins approaches Bones, Cam and Angela who are having a coffee, the position of Angela and Bones changes instantly. (00:30:50)

The Doctor in the Den - S4-E18
Continuity mistake: Around the 37-minute mark Bones approaches Cam with an update on the case. When she does, Cams position alters between shots. A hand suddenly appears by her mouth/chin. (00:37:30)

The Science in the Physicist - S4-E19
Continuity mistake: When Bones and Booth are looking at the meteorite for the 1st time, they are approached by Chris who folds his arms to talk to the pair. When the shot changes, his hands are now in his pockets. (00:07:50)

The Science in the Physicist - S4-E19
Continuity mistake: When Bones and Booth get trapped in the resonance chamber, the position of Booth's hands over his ears changes back and forth between shots. (00:34:30)
The Science in the Physicist - S4-E19
Continuity mistake: Bones finds a spot of damage on the chair (front side, about 4" down from the top edge). Yet later, the chair is without any damage.

The Cinderella in the Cardboard - S4-E20
Continuity mistake: When Daisy convinces Sweets that she's not cheating on him, her arms move back and forth from his shoulders to around his neck. (00:37:05)

Continuity mistake: When interviewing Lexi she puts her arms up and plays with her hair in one shot but then in the next her arms are down. (00:28:30)
Answer: Answering my own question here but, having contacted various people involved in the production of Bones including Kathy Reichs, Hart Hanson, Eric Milligan, and Deirdre Lovegood who portrayed Taffet onscreen I finally have the answer. No-one know how she did it due to her constantly working alone. And she never revealed this information before her death.
Ssiscool ★