I've just done a search for this same white line around images problem and came across this so thanks for all the above suggestions.

To fix it I needed to add:
GraphicsDevice.SamplerStates[0].MagFilter = TextureFilter.Point;
Btw, any takes on the "title safe issue"?
It's a serious pain if you come from PC development where title safe isn't really an issue. I ended up redesigning my game to have a panning camera so that all the arena could be seen within the title safe limits. Having a fixed camera would have restricted me to a tiny arena.
Another alternative is to render your display to a texture and then have an option that allows the user to resize this to fit perfectly on their display. (One of those "resize until the dots are at the corner of your screen" affairs.) This way you get to use the full available screen area while also ensuring that nothing is off screen.
I know that's not always a popular option mind so I'd be interested in what others think as I plan on using it in my next project on the 360.