In the scene where Trinity is running on the rooftops and flys through the air into the other building, she spins in mid-air and breaks through the window face up with her back to the ground. In the next scene, it shows her breaking through the window face down and rolling forward down the stairs.
When you see Trinity "spinning" through the air, look at the background...
You should notice, that it is in fact the camera which is spinning around Trinity!
The camera passes over the top of her and right before she breaks through the window, the camera is upside down on the opposite side of her.
This is not a slip-up.
I noticed this too, its not too hard to see, is it? At first I though the camera was a little weird with its movements. The second time round I noticed, it spinning around her (hence the sight of ground, walls, sky -or something in that order-), so instead of rewinding, watching, rewinding, slow mo, rewinding and commenting, watch it properly WITH the backround! Its not Trinity's flying spin, but the camera's flight-path spin!
The Matrix is not REAL. The REASON she can fly in the first place is that it is NOT real!!!! SO it does not matter if she is flying sitting straight up!