I'm not sure how to answer this because what you're describing is the break-up of the 3D effect, which is kind of a fundamental potential problem with the 3DS. This can happen for any number of reasons when you're playing. The 3DS outputs two images (one for each eye) and the phenomenon you're describing is what happens when your eyes aren't able to fully combine them together. This can happen for any number of reasons: the action is scrolling too fast relative to the framerate, the game is throwing more fields of depth at you than your brain can understand, glare on the screen (which can confuse your eyes' perception of the depth of the game images), too much flat color (depth of field gets lost in flat unchanging colors), and, mostly commonly, the viewing angle of the 3DS relative to your eyes being non-optimal.
The new 3DS has one specific improvement in this regard: it uses eye tracking to adjust the 3D output relative to your eye position. This should make it somewhat easier to hit the 3D "sweet spot". Hands-on impressions have commented very positively on this feature.
Also, one can't discuss 3D on the 3DS without mentioning the 3D slider. As I listed above, the 3D effect can break-up for any number of reasons. Lowering the 3D slider reduces the 3D effect by making the two images outputted by the 3DS more similar to each other, and thus making it easier for your eyes to combine them. This is a catch-all solution. I use 3D all the time and, unfortunately, is not uncommon to have to adjust the 3D on the fly in some games to keep the effect working properly.
I hope this was somewhat helpful. I didn't know exactly what starting point you were coming from in asking the question so I tried to be comprehensive.