I hadn't even thought of the possibility of running into radioactive exhaust from the ship in front of you. I doubt it would be a problem, but I can't prove that.

Whether or not propulsion systems would improve substantially over a century in the time frame you mention, or not, is another question I don't think anyone can answer now. Technology would no doubt progress, but the laws of physics are fixed, we don't really know if any of the advanced fusion-based propulsion systems now being considered could actually work. The growth of technolgy over the last two centuries has been so explosive that we have been psychologically brainwashed into thinking that the growth willl be exponential for the indefinite future. Maybe not, technology may plateau, maybe not this century, but perhaps two or three ahead as we start approaching fundamental physical limits. As you point out, our rockets are not fundamentally different from the V-2, and although fission propulsion (Orion nuclear pulse or Nerva-type reactor) is forseeable, we have no guarantee that physics and engineering will take us much further. And we certainly have no guarantee that the relativistic barrier will ever be broken.

Come to think of it, the only really fundamental engineering breakthrough we've had since the harnessing of thermonuclear explosives was the invention of the transistor/integrated circuit. The only major technology we have today that would have really been a surprise to a '50s physicist would be the computer chip...and perhaps the laser.