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" _I studied for about 2 or 3 years._ " is natural while " _I studied for
about 3 or 2 years._ " is not. Notice that the time period length sequencing
is from shortest to longest.

Yet, in this audio clip at _www.bbc.com_ the sequencing is longest to shortest
[How Japanese Police Confront Violence](http://www.bbc.com/news/av/world-asia-
pacific-38534288/wrapping-people-in-futons-how-the-japanese-police-confront-
violence) at the 20-second mark you can hear in the background the officer say

警察学校に一年もしくは半年...

(1) it is natural to list lengths of time in reverse numerical order?  
(2) ALSO, notice that he just said "一年" instead of "一年間" which contradicts my
understanding.

I definitely would have said:  
"警察学校に半年もしくは一年間..."

and this is definitely unnatural, correct? Both cannot sound natural?

What about "２、３本ぐらい飲んだ" vs. "３、２本ぐらい飲んだ"? Which is better?
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Is "... 半年もしくは一年間 ..." unnatural?
I think you are basically correct. 警察学校に半年もしくは一年間 sounds fine as Japanese.

However, it depends on the context.

I can understand what the speaker wanted to say. In this case, he said,

> "Japanese police officers took kendo or judo training course, for basically
> one year, or for half a year in some exceptional cases."

The majority of police officers took a one-year course.  
A minority of police officers took a half-year course.

He wanted to say "one year" but if he said so, he realized that it would be
inaccurate about some of the students/police-officer-candidates. So he added
the last bit to clarify that there's a half-year course.

That's how I interpret it.

About the 1年/1年間 difference, again you're basically correct. In some or many
contexts, however, 1年 can be used for 1年間. I mean, 間 can be abbreviated in
some/many cases.

Hope this helps!
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I don't think his way of saying 1年もしくは半年 is strange in particular.

  * にさん is [a fixed phrase](https://japanese.stackexchange.com/a/21681/5010) that roughly means "a few", and reversing it (さんに) is fairly strange. But 1年もしくは半年 is not using a fixed idiom, and it does not sound as strange as さんに年 or ごし本くらい飲んだ.
  * This is a spoken sentence, which is not as organized as a written article. In speech, you may say something like "one, ...or maybe a half", adding "half" as an afterthought. His way of speaking is similar.

This 間 is optional, and it tends to be omitted in speech. Few people say
10分間待って in speech.
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