When Obadiah removes Tony's arc reactor, Tony starts to bleed from around the socket and I can't understand why.
It's only a slow and small amount of bleeding but I still can't help but question why.
Can anybody offer any rationale for this?
Remember the purpose of the Arc Reactor in his chest; it's there to power an electromagnet which keeps fragments of shrapnel from migrating into his heart. With the Arc Reactor gone, those fragments are now beginning to do their damage. Hence the bleeding.
The obvious plot hole is that putting in the "backup" Arc Reactor wouldn't undo the damage the shrapnel has done, it would just stop additional damage; he'd be just as hurt after putting his old reactor back in.
I just watched it in full-HD, the dark coloration you are referring to as possible blood is actually burnt parts of Tony's shirt, if you notice the remover tool burns through the shirt, this burnt part of the shirt is dark and from far away does kind of look like blood.. So not shadow play, burnt white t-shirt.
I agree there appears to be bleeding. While Obadiah is sitting next to Tony on the couch talking about the arc reactor, if you watch you can see the "darkness" spread and grow deeper in color.
While I have nothing authoritative to back this up, I would presume this was caused by the "rough" manner in which Obadiah disconnected the arc reactor from the socket. He doesn't take any care in disconnecting it and just jerks the power connection free.
While the flesh around the socket is normally healed, this rough treatment may have caused some separation between the flesh around the socket and the socket itself. Odds are this is non-life threatening and would stop by itself within a short period of time, but it is enough to show on the white shirt that Tony is wearing at the time.