Sorry for the double post, there was an error message and I didn't realize it was already posted. Also, I can't upload the screenshot here, so here's a link to it:
http://i.imgur.com/9OyXsBC.jpg

I believe this one has been fixed in the recent updates, in the entry "Fixed spawning bug for vehicle where angles were in certain cases inverted"

I think this was caused by the solar panels on the medium rover. So far, I couldn't reproduce this bug anymore!

Just a quick update, now that I have a nice Medium Rover and more instruments, sometimes I still get impossible tasks with the Dynamic Mission Generator.

Most of the times, it's due to incompatible instruments and category of tasks, like using EAS on a Rock, APXS on Atmosphere, MICRO on Subsurface (instead of DAN), and so on. Sometimes, I have the option of using different instruments for the same tasks, and usually there's only one that can really be used to complete it.

Edit: Also, one more suggestion regarding the dynamic missions. The markers for them only appear on the HUD with the "Filter by mission" turned off, but by doing so, sometimes, the HUD can become a huge mess of markers from different missions and tasks not related to the main misson or to the dynamic missions. I think it would be nice to have an option to turn on the "Filter by mission", while keeping the Dynamic Mission markers on screen.

I have the same problem. Usually, the marker don't show up when the rover don't have the correct instrument to perform the task. But in this case, my rover have almost every instrument available installed, with the exception of the DRT. And even after sending a rover with DRT, there was still no visible objective.

I can confirm this. In my tests, it's usually the left panel that falls off first, and then the right panel. It even happens on flat terrains, with no dunes or stones nearby. Most of the time, I can't even travel 50 meters before they start falling off. It's really easy to see this happen in the Rover Yard.

I don't think it should be an randon event or based on distance travelled. I guess they are suposed to be fragile, but they are meant to last at least one mission. I think they should only break if you are not careful enough and hit them in a rock.