Spectrum = gamme. The idea is that any given court decision falls somewhere within a range of persuasiveness or authority, from least persuasive/least deserving of respect to most.

And because the subject here is how judges in the common-law system take the decisions of other judges into consideration, I think that using the word "respect" in FR might be confusing or misleading here, even though it's usually a good translation of the EN "respect."

Here's why: If you talk in FR about respecter le jugement/la décision d'un tribunal, it sounds like you're talking about respecting the conclusion it reached for that case: in other words, is the appellate judge going to let that decision stand, or reverse it? But, speaking as a US lawyer, I don't think that's what this is about.

In the common-law system, unlike the FR civil-law system, the judge hearing Case X may considers the decisions of other judges in similar cases (let's call them past cases A, B and C), in order to decide whether to apply that same reasoning to Case X.

So what this text seems to be talking about is the degree to which the judge in Current Case X is going to find the reasoning of other judges in cases A, B and/or C persuasive, and thus apply that same reasoning to reach a decision in Case X. It's not about reversing cases A, B or C. It's about whether or not the judge in Case X is going to reach a decision, in Case X, that happens to be consistent with cases A, B and/or C.

So I think this requires rephrasing: Le pouvoir de persuasion [d'un jugement antérieur/d'une décision antérieure] donné[e] se décline sur une gamme, selon sa nature...

BTW I understand this to mean not an absolute spectrum/gamme, but one that is relative to the case in question. In other words, Past Court Decision A might be highly persuasive (deserving of great respect) in Current Court Case X, but hardly persuasive at all in Current Court Case Y, due to the different factual and legal issues at play in cases X and Y. I'm just mentioning this so you can avoid turns of phrase that might suggest that any given decision is inherently deserving of respect by all future courts in all cases.

FYI, the second bit, about caution, refers to the fact that in the US and perhaps all common-law jurisdictions, appellate courts hesitate to reverse lower-court decisions when the issue for which reversal is sought depends on the credibility of a witness. Appeals courts do not see witnesses testify; trial courts (tribunaux de 1e instance) do. So appellate judges tend to let decisions stand if the basis for the decision was whether someone's testimony was credible, since the trial judge was there and saw/heard the witness testify.



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Note added at 2 days 9 hrs (2019-07-10 18:43:25 GMT)
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PS @ François Boye:

"La lutte contre la fraude vise à protéger les intérêts financiers des Communautés européennes... contre tout comportement illégal. La forme que peut revêtir un tel comportement varie beaucoup et se décline sur une gamme allant du non-respect d’une norme de droit communautaire, par erreur ou mégarde, jusqu’à des actes intentionnels, voire criminels, souvent perpétrés par des réseaux organisés."

Commission des Communautés Européennes, Protection des interêts financiers des communautés et lutte contre la fraude - rapport annuel 1998, Page 10 section 1.1 (https://eur-lex.europa.eu/legal-content/FR/TXT/?uri=CELEX:51...