Are there any exceptions to the rule of adjective order?

Yes; in some cases, the "improper" ordering is more popular than the "proper" one. Occasionally, there's not even a preference for any order between two adjectives.

According to Forsyth, color comes after shape:

Quality > Size > Shape > Color > Provenance
_{The Elements of Eloquence: Secrets of the Perfect Turn of Phrase}

However, in real life, "yellow rectangular" has 99,200 results while "rectangular yellow" gives 94,200 results. The same pattern appears, more drastically in fact, when looking at the results in Google Scholar. "Yellow rectangular" has 2,090 results as opposed to "rectangular yellow" with 489 results.

Ngrams indicates it's been a battle:

(Is it really a law when it can change so often?)

In other cases, it's just anarchy:

_{[Data from COCA]}

According to Forsyth (I think), those all should be opinion-size, i.e. 2+1 as in the second column — but all of them are mixed, and some go pretty strongly the other way.

_{Big bad modifier order}

Exceptions are certainly possible. The linked article even mentions one: "Big bad wolf."

Furthermore, it seems to me that adjective order has a lot more freedom if the adjectives are loosely linked with a comma in between them. The article claims no one would say "old silly fool", but I think it would be unremarkable for someone to say "old, silly fool."

Here's a relevant Language Log article by Mark Liberman that discusses the topic: Big bad modifier order

The quoted sentence only seems to make sense to me if we conflate actual descriptive rules of grammar and syntax, as identified by linguists, and "zombie rules" that are prescribed, but that don't actually describe usage accurately, such as "don't end a sentence with a preposition" or "don't start a sentence with a coordinating conjunction." The latter are obviously highly "violable"—not only in informal speech, actually, but even in educated writing (but if you point this out to a prescriptivist, you'll often be told something like "great writers are allowed to break the rules").

But in general, linguists don't expect actual laws of syntax to be violable at all. For example, articles such as "the", "an" and "a" must come before the associated noun ("the child") rather than after ("child the"); this is not optional at all. Compared to an actual "law of syntax" like this, the adjective-order rule is actually pretty violable.

The adjective-order "law" also seems to be acquired by children much later than the law governing the word order of nouns and articles: there's an anecdote about J.R.R. Tolkien writing as a child of seven about "a green great dragon", and being corrected by his mother. Could you imagine a child of this age writing about e.g. "great green dragon a" or "great dragon green a"?

A side point: in my experience, the generally known rules for adjective order in languages like French, Italian or Spanish are also over-simplications. In fact, I'm not aware of any language that has completely, rigidly unviolable rules for ordering adjectives that belong to the same general syntactic category, but you may be able to find an example if you read the literature (I haven't, but the linked Language Log post points to The Cross-Linguistic Distribution of Adjective Ordering Restrictions by Richard Sproat and Chilin Shih).