Auditor,
Good job on thinking about practical problems.
If we make the assumption that the frames of reference of "now" and "then" are roughly the same over time if we are time traveling to and from this planet only and we also assume that all of the laws of physics remain the same (a very good idea) I can imagine some other issues that are equally problematic.
Let's imagine that our time traveler wants to go from December 2014 to D-Day, June 6th, 1944 to have a look at a historical event. In order to orient ourselves to our local frame of reference we'll look down on the solar system from above the Earth North Pole. We can then call movement to our right as "east" and movement to our left as "west."
In December, as we look down on the Earth, we see it moving anti-clockwise to our right (east) with an orbital velocity of +30 km/sec. That's when our time traveler leaves for June 6th, 1944. Our assumption that all physical laws remain the same implies that our time traveler must carry along with him a linear velocity of +30 km/sec with respect to the frame of reference.
He arrives at June 6th, 1944. Earth, in June is ~180 degrees further along it's orbit than in December. From our top down perspective it is moving at -30 km/sec (west). If the laws of physics hold our time traveler will either splat into the Earth at ~60 km/sec (about 1.3 million miles per hour) or skim along the atmosphere. If his mass remains at about 1000 kg (vehicle, components and passenger) he'll auger in with a kinetic energy of ~.4 kT TNT equivalent (a small tactical nuke) or, if he skims the atmosphere, be seen on Earth as a very bright meteor.
[I didn't quite pick 1000 kg from the air. One would-be time traveler here claimed that his gadget weighed in at 500 lbs (~225 kg) and his vehicles was a Chevy pick-up (~1000 kg).]
In the above example I purposely chose to make the problem obvious. The problem really isn't solved if we leave on June 6th 2014 and arrive on June 6th 1944. The orbital mechanics of just the Earth-Moon system are so complex that we really can't predict the exact location of the Moon through direct computation. Predicting the exact location of the Earth in 1944 from 2014 given the Earth-Moon-Sun-Saturn-Jupiter system is a huge problem. Even if we are extremely accurate and the gadget only hits the Earth at 20 km/sec it is still a big problem for the gadget and its contents.
Time travel, if possible may well require advanced space travel. One might have to travel to the general vicinity, arriving in space, accelerate to match the target's velocity and then land.