
Harbingers in a Fountain - S5-E1
Continuity mistake: Brennan has just returned from Guatemala and is back at her office. She meets Booth and the two hug. The way they hug each other differs between shots, most notably the position of Brennan's right elbow on Booth's shoulder. (00:04:00)

Harbingers in a Fountain - S5-E1
Continuity mistake: When using the ground penetrating radar, Bones says there is no such thing as a psychic. When she does she alternates from looking at Booth to looking at the radar instantly. (00:05:50)

Harbingers in a Fountain - S5-E1
Continuity mistake: When the doctor tries to ambush Bones, he has the scalpel raised at head height. Camera change and now it is much lower. (00:29:30)
Harbingers in a Fountain - S5-E1
Continuity mistake: Bones gets stabbed with a scalpel in her arm and it's bleeding profusely. However the next day she has a short sleeve top on and there is no mark or bandage on her arm. (00:30:50)
Harbingers in a Fountain - S5-E1
Continuity mistake: When Angela is checking the facial recognition, the photos actually stay the same, but just rotate spots.

Continuity mistake: The amount of grime on the CIA badge changes between the long and close-ups. (00:13:40)

Continuity mistake: Bone states that she will never have to fly coach When she does, she keeps her mouth slightly open. When the camera changes, her mouth is closed. (00:17:00)

The Plain in the Prodigy - S5-E3
Continuity mistake: Near the start, Cam is carrying sunglasses in her hand; suddenly they are on her face. (00:03:20)

The Plain in the Prodigy - S5-E3
Continuity mistake: When Sweets comes to look at the rocks he puts his gloves on. Camera changes, and he's putting his second glove on a second time. (00:15:20)

The Plain in the Prodigy - S5-E3
Continuity mistake: The girl says that she saw a "full on Amish guy" who looked pissed. When she says this to Booth, he hand disappears from her chin instantly. (00:24:40)
The Plain in the Prodigy - S5-E3
Continuity mistake: When finding out that the key cover broke Levi's hand, Bones is holding a bone in her hands and examining it. When the shot changes she isn't holding the bone any more. (00:34:30)

The Beautiful Day in the Neighborhood - S5-E4
Continuity mistake: At the start we see Nate having a drink from his cup and then lower the cup. When the shot changes he's drinking from the cup again. (00:01:00)

The Beautiful Day in the Neighborhood - S5-E4
Continuity mistake: When Hodgins holds up the evidence bag with the bullet in, the bag flips round in his hand instantly. Note the position of the bullet itself and the label on the bag. (00:13:00)
The Beautiful Day in the Neighborhood - S5-E4
Continuity mistake: Near the end, as Parker drinks his milkshake, its contents rise & fall (not counting his drinking some). Also, he moves the glass about enough to illustrate that it's fake - it would have spilled, the way he handles it.

A Night at the Bones Museum - S5-E5
Continuity mistake: The mummy is in direct sunlight with no shadows on him when Cam first walks up to examine him. When Bones and Booth walk up to him, a few seconds later, the right side of his face is in the shadows. (00:04:00)

The Tough Man in the Tender Chicken - S5-E6
Continuity mistake: When Booth is on the phone to Darma asking if they are missing a man that looks like a chicken, the way he holds the poster changes between shots. (00:07:40)

The Tough Man in the Tender Chicken - S5-E6
Continuity mistake: As Hodgins says he will chip in for the pig, the item he's holding has 4 items sticking out of it. When the shot changes, these items change position. (00:31:00)

The Tough Man in the Tender Chicken - S5-E6
Continuity mistake: The position of the pig picture Angela places on the item Hodgins is holding changes places. First it's resting on 2 spikes then 3. (00:31:05)

The Tough Man in the Tender Chicken - S5-E6
Continuity mistake: The amount of paint on Wendel's hat keep changing drastically. Most noticeable is when Bones stops him spinning and leans him forward. (00:34:15)

Continuity mistake: When Angela tells Gordon about the python, Gordon has the sandwich up to his mouth in one shot and lowered in the next. (00:23:40)
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 ★