So, I'm a bit late to this one, but seeing as the question popped up as being related to some other ones I've looked at lately, and the accepted answer is wrong, I thought I may as well chime in.
could the radiation hitting the unshielded side cause structural damage and/or harm the passangers?
No structural damage, but it will kill everyone on board and probably trash all the electronics, too.
Should additional shielding used on the cabin's side walls?
You could, but it would make more sense to use a slightly different ship design that avoids the flipover. That shielding is heavy!
Or would the minimalist shielding against galactic cosmic rays suffice for a short period of time?
It doesn't make sense to talk about "minimalist shielding" for GCRs: they're too hazardous for that. They are, however, amenable to magnetic deflection in a way that neutral gas particles in the interstellar medium are not. Your GCR protection probably won't save you.
The problem is that although the interstellar vacuum can be pretty vacuuous, it ain't empty. Space around our star is unusually low density thanks to the explosion of the Geminga supernova blowing must of the interstellar medium away. You might find one hydrogen atom per 100cm3. A ship travelling at .7c, therefore, can expect to have 2.1x108 hydrogen atoms hit every square centimetre of its cross-section every second. Note that these are mostly neutral atoms, so magnetic shielding ain't gonna save you from them.
The paper Radiation Hazard of Relativistic Interstellar Flight looks into more detail at what this rain of high-energy particles will do to unshielded humans. It ain't pretty: the radiation dose is about 104REM per second. That's a lethal dose in less than a tenth of a second, and more than enough to ruin electronic systems throughout the ship. A five minute turnaround guarantees that the ship will be sterilised and that all computers will be thoroughly wrecked.
Shielding against this radiation isn't impossible... somewhere between 10 and 30cm of titanium should do the job, or a metre or two of water. That's a lot of shielding though, shielding which isn't obviously present on any part of the ship other than the big stack of debris shields at the end:
and remember that every part of the ship that contains vulnerable things (people, other living things, electronics, antimatter) would need to be shielded. All that dead mass for a tiny moment during flipover. What a waste!
One of the technical advisors for the design, Charles Pellegrino, should have known better. He'd been involved with a previous design, Project Valkyrie, which similarly used a tension structure instead of a rigid hull, and antimatter rockets. The major difference though is that the Valkyrie design had two engines at opposite ends of the ship, one for boosting, one for braking. This gives some redundancy, but also means that you don't have to flip around and irradiate yourself at the midpoint of your journey.
Really, all the Venture Star needs is to dock the laser sail at the debris shield end, and to have an extra bit of laser shielding at the other end to protect the rockets during the laser boost phase. It isn't like the debris shield is big enough to protect the laser sail anyway, so there's no loss of performance, and it comes with the benefit that everyone gets to live.