Hi, Billy !
If I remember rightly, there is a 64-k-limit or so, to 3ds (->TooBig1, TooBig2... in C4D). If the object divides to sub-objects, the limit seems to apply to those, not the entire group. Perhaps that's why dadt's Vicky passed the test.
Export scripts screwing up files, when they triangulate polys, especially when polys have an extremely short side or coincidences near zero (rounding errors ?), is a daily worry. Resizing the objet by *5 or 10, before export might fix it. Algorithms aren't very intelligent.

Sometimes, when things are running too well, I simply foul up gones manually, which gives such peaks - I'm rather efficient at that sport ! ;-)
Things like inverse numbering of points (screwed polys), open faces, unclosed polys, doubled points, offset a micron, overcrossed bevels...
With some ancient renderers, it was possible to show such spikes, even using a good mesh : For example by grouping it inside an other object, and have the cam's projection plane center cut a vertex. T'was especially efficient in animations...
My artistic creativity has no limits, to do the job :-) - I don't know if such applies here.

Did RemcoVANMERM send the file to Rodluck for a try ?
Did they get any farther with this spikes question ?