Plot hole: Parker gains access to the external room using a valid security card, they figure out the CEO's passcode which opens the burn room door...and yet the room inside is still protected by a swarm of lasers. Was the CEO supposed to dance through the laser sensors like Parker does every time he goes in?
Continuity mistake: When Sophie is "shot", the two gunmen duck down immediately. When we see the flashback later, neither of them duck. One gunman walks away, while the other is revealed to be Elliot, who looks down over the barrier at the crowd for a beat before leaving.
Deliberate mistake: When filming the fake movie with Sophie playing the nun, many holes are made in the door, but when she slowly kneels to the ground, there isn't a hole behind her, so it seems like she's been miraculously saved. But as the scene continues, the nun starts to bleed and dies. Technically, they couldn't safely put a squib that close to her. (00:21:15)
Character mistake: Upon finding the Spanish flu virus missing, Hardison freaks out about it killing 50m people 100 years ago, saying it would be even more deadly today due to the higher population. There's no reason to think so - the death toll in 1918 was massively exacerbated by the aftermath of WWI. Not to mention today we have vaccines, plus most deaths then were actually caused by bacterial pneumonia, which today is easily treated with antibiotics.