"Is the bridge at a funny angle?"
Short answer: yes.
Long answer: The bridge set was obviously designed and constructed to be as easy to film in and around as possible, with as little getting in the way of the actor's movements or visibility as possible. As such, the door to the turbolift is set off center, so that Kirk doesn't block the entrance visibly, and the incoming and outgoing crew members don't trip over the captain's chair when moving about the bridge. In-universe, I have always pictured the bridge interior matching the exterior, with the turbolift directly behind Kirk's chair, which faces directly towards the viewscreen, pointed directly at the ship's foreward bow. It doesn't make sense for the viewscreen to be off kilter, or for the turbolift to be either. Sometimes the best solution is the simplest. When I get a chance, I'll post a diagram of how I imagine the bridge layout to actually be.
EDIT: I did a quick drawing of the TOS bridge in both configurations. Please forgive the crudeness of the drawing, I hope you can make out what I'm trying to illustrate. Figure A is the bridge set as it appeared in TOS. Figure B is the way I picture the bridge actually looked. The main difference is the turbolift has shifted from aft port to directly aft, although you'll notice Figure A has four bridge stations on one side and two on the other, while figure B has three bridge stations on either side. Also, figure B has rotated the bright red hand railings surrounding the central command area by 45 degrees. I much prefer Figure B myself, but it isn't exactly canon...oh well.
Short answer: yes.
Long answer: The bridge set was obviously designed and constructed to be as easy to film in and around as possible, with as little getting in the way of the actor's movements or visibility as possible. As such, the door to the turbolift is set off center, so that Kirk doesn't block the entrance visibly, and the incoming and outgoing crew members don't trip over the captain's chair when moving about the bridge. In-universe, I have always pictured the bridge interior matching the exterior, with the turbolift directly behind Kirk's chair, which faces directly towards the viewscreen, pointed directly at the ship's foreward bow. It doesn't make sense for the viewscreen to be off kilter, or for the turbolift to be either. Sometimes the best solution is the simplest. When I get a chance, I'll post a diagram of how I imagine the bridge layout to actually be.
EDIT: I did a quick drawing of the TOS bridge in both configurations. Please forgive the crudeness of the drawing, I hope you can make out what I'm trying to illustrate. Figure A is the bridge set as it appeared in TOS. Figure B is the way I picture the bridge actually looked. The main difference is the turbolift has shifted from aft port to directly aft, although you'll notice Figure A has four bridge stations on one side and two on the other, while figure B has three bridge stations on either side. Also, figure B has rotated the bright red hand railings surrounding the central command area by 45 degrees. I much prefer Figure B myself, but it isn't exactly canon...oh well.

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