Eagle cad netwires not connecting

All of the library components have pins on a 0.1" grid. If you change the grid to, say, 0.05" and place a part such that its pins are no longer on the 0.1" grid, then neither will the pins be on that grid.

You must either then route on a 0.05" grid, or move the part back to a 0.1" grid. You can do that by selecting the Move tool and Ctrl-clicking on the part.