I agree, you should check first for
1. overlapping elements
2. connectivity (elements not connected with the part)
after checking this, i would use the ORIENT ALL tool and check the mesh statistics.
if this doesn't work either a sort of long way to find this trias that I would use is:
go to mesh -- mesh tools -- orient elements.
there, on the REFERENCE select an element with the 'correct orientation' and then on the checkboxes below that select the that reads: Connected elements WITH the same orientation.
Click SEARCH and it would show lots of elements selected but probably not to the whole part. Here, what i would do is to create a new layer to store 'temporarily' all of these 'OK-oriented' elements (create a layer and then assign the already selected elements into the new layer).
Turn this layer off, and do the same method with the rest of the elements that you have left...until you find the elements that are not oriented the same way.
I know it's a long way to go, but you might find it sooner than later, and to be honest with you I think you will be fine after checking overlapping, unconnected elements and doing the orient all tool. I just wanted to give another option...you're probably gonna be dreaming triangles after this if you choose to go this way... 😃
good luck...
Hugo Herrera