Priorities

There are rules to the order of adjectives.
This is an excerpt from my grammar book:

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We order adjectives according to their meaning.
This is the normal order:

1 Opinion (how good?)
2 Size (how big?)
3 Most other qualities
4 Age (how old?)
5 Colour
6 Origin (where from?)
7 Material (made of?)
8 Type (what kind?)
9 Purpose (what for?)

I never saw Ed's list before but it is interesting and I will think about it. In the case you are asking about, I think the best order is benign first, followed by media...., then cystic.

I'd definitely put "benign" first.

I agree, benign mediastinal cystic teratoma. The most important thing to most involved, including the patient, is the benign nature of the tumor. Think of that as an overarching adjective. Then we get more specific. If mediastinal refers to a part of the body, I'd say put that second, as I have above. If however, it is descriptive of the tumor itself, as cystic obviously is, then it really is a toss-up between cystic and mediastinal.

That list is freaky. No way can we expect ourselves to be ruled by such a thing. How easy it would be to come up with counter examples that do not follow it. Having said this, it has always been interesting to me how different languages choose different word orders, especially in their adjectives. I'm not sure I could articulate the English language rules on this.

our english teacher had repeated -and made us repeat- the meaningless "n s sh k" sounds for about a month without telling us what it was. later he told us that it was the order of the adjectives put before a noun.
number size shape color
it's a shorter list and not very similar to ed's, but it's simpler and easily remembered. at least after repeating "n s sh k" for a month =)

As a board certified pathologist for over twenty years, I claim that the only order that sounds right is "benign mediastinal cystic teratoma." It's probably just a matter of linguistic custom and conditioning, but if anyone used any different word order, I would know he or she was not a pathologist, because a pathologist simply would not say that!

As Ed says, there is indeed a definite order for adjectives.
I teach my students the mnemonic OPSASCOM to help them remember :

OPinion
Size
Age
Shape
Colour
Origin
Material

As you can see, this differs slightly from Ed's but most people find OPSASCOM a useful tool to help them remember...