At a level crossing which goes across the road at an angle rather than dead perpendicular, the groove next to the rails will catch your front wheel which may or may not result in you getting thrown off and/or winding up with a bent rim.
Only if you're riding through it completely not paying attention. I've got exactly such a crossing near my house, and I ride over it very frequently, both on a mountain bike and on a skinny-tire road bike. And I've never once had the slightest issue, because I pay attention to where the tracks are and momentarily go at an angle to make sure I cross over them more perpendicularly. Just takes a slight swerve at the right time, really.