There will be no manned Mars missions: radiation.
Not a showstopper, but definitely a problem that needs to be addressed.
It's not per se a deadly amount of radiation, but it does increase the astronaut's risk of cancer. A quick calculation once suggested that a trip to Mars and back would give you an increased risk of cancer roughly equivalent to smoking a pack of cigarettes a day. Robert Zubrin once quipped that the answer is simple: pick astronauts who are smokers... and don't send any cigarettes with them.
The problem is that no one has any doable idea to stop it.
To the contrary, this has been analyzed a lot, and there are many ideas for how to stop it. With respect to the current topic, one idea is simply to use a more effective engine, and make the trip faster to shorter the exposure.
And this isn't the milk toast radiation we get around the Earth. This is the really nasty stuff from the rest of the Universe.
Really there are two types of radiation to worry about. One is solar protons (coronal mass ejections, or "CME"s), and the other is galactic cosmic rays ("GCR"s).
And if you are lucky, you won't run into a solar flare on the way.
That, at least, is a solvable problem. The protons from a solar flare can be seen in advance, and last only a day or so. You can make a small portion of the spacecraft a "storm shelter" with enough shielding to stop protons (light elements are best for stopping protons; water, for example, is a great dhielding material. GCRs are harder to stop). It would be too heavy to shield the entire ship, but the astronauts can stay in their shelter for a day or so.
GCRs you simply have to live with. This risk is cumulative, so the solution is to go as fast as possible.
Aside from the pretty lights, it is really nasty radiation. Don't forget to protect your space craft's instruments, they are more delicate than even you.
Protecting electronics is something we already know how to deal with. We have robotic probes that have been operating for literally years in deep space, not to mention one probe that routinely dips into the ferocious radiation environment of Jupiter's radiation belts.