Do you mean by rotating the part and observing the variation with a microscope/projector?
Without actually seeing a part and the specifications, it's hard to say. I'm assuming that a standard optical comparator isn't appropriate for all of what you're trying to measure.
I've contacted several equipment suppliers, and also one measurement laboratory. My understanding was that the only way to measure these tolerances was by using a tactile system. But this solution is quite expensive, and it makes the inspection very time-consuming. That's the reason why I want to be sure that it's the only way.
Perhaps a trip back to the drawing board is in order. If the people who designed these parts are available, you need to sit down with them and ask them how you're supposed to measure what they've designed. The answer is likely to be a blank stare, but designers need to understand that they have to consider the state of the art in measurement (and its potential costs) when they do these things. Verifying measurement capabilities--both yours and your suppliers'--should be part of the design process. I know that might not be particularly helpful in getting you out of the fix you're in presently, but it's useful information for others reading this.
Most parts are actually drilled cylinders (i.e. tubes..) and the wall thickness is quite small (0.5 mm) and the surface to be checked for flatness are the extremities... As Jim mentioned, do you think it is possible to use optical flats on such small parts?
Again, without seeing the parts, it's hard to say. If you're talking about measuring flats on the OD of a cylinder, then optical flats probably won't work. If you're drilling on the ends of a cylinder, it might work, depending on the surface area available. You also have to consider the light source when using optical flats; it needs to be monochromatic (waves of a single length) in order for optical flats to be effective. It's a fairly tricky business if it's to be done correctly, and best avoided if there are other options.
I have also requirements on paralellism and perpendicularity on some of these parts, do you think they could also be measured with a vision system at that accuracy?
I don't know. If you've got a cylinder with a hole drilled through it lengthwise, and you need to measure the parallelism of the ends and the perpendicularity of the bore, you might be able to make a fixture for it, but it would probably involve (A) considerable expense, and (B) only attributes data.
Do you think it's better to have a non-contact solution?
Only if contact methods aren't feasible. Direct measurement is usually the best option if it can be done.