So I found a vase on thingiverse and I wanted to print it, so obviously I did. I used craft ware to slice the model using there 'vase mode', and sent the Gcode to my Anet A6 printer. In the end I found weird underextrusion (I think that is what happened) at the starting points that seem to have appeared. I don't know what to think of this and I don't know what happened or how to fix it.
This sort of failure is best diagnosed by observing the failure. It probably isn't underextrusion, there is no reason to get variation in extrusion just along one edge.
Did you really get a proper vase-mode? You can check in your slicer, or with gcode.ws and make sure that each layer only occupies a fraction of the part, with many small steps (rather than one step after printing a slice of the whole part)
It seems the failure is close to a sharp transition in the wall. Have you got enough cooling, or a low enough extrusion temperature? It could be that the plastic viscosity and surface tension are conspiring against the shape. Printing slower might possibly help too (both on the failure, and to allow the part to cool between layers).
Finally, you might have a mechanical problem which is interfering with the print just at this point, and that might include the extruder binding in some way. This could be hard to spot during the print, so check over all the moving parts, and all the fixings.