Consider the following passage from CGEL (p. 458, boldfaced emphasis mine):
We look first at the contrast between nominative and accusative case, where we find a considerable amount of variation and instability in the system. There are a number of constructions where the nominative is associated with formal style, the accusative being strongly preferred in informal speech and writing. Because of the tendency of older prescriptive grammar to accept only formal style as 'grammatically correct', there has been a tradition of criticising the accusative alternants, and the stigmatism attaching to such accusatives has given rise to a certain amount of hypercorrection, with nominatives being used in constructions where the traditional rules call for an accusative. Or at least this is the situation with the personal pronouns and determinatives: with interrogative and relative who the reverse situation obtains, the accusative whom being the case associated with formal style.
I do have a general idea of what they might mean by this 'instability', but I could be missing something, too.
First of all, I think the particular instability mentioned here is a synchronic, as opposed to a diachronic, feature of English syntax.
It would be (I think?) easy to understand what a diochronic instability is: if there is some feature of language that is currently undergoing a change, then that feature is currently diochronically unstable.
But a synchronic instability should be a feature of language at a time. In other words, it should be something that can be described without referring to features of language at two different points of time.
One example of synchronic instability that I (think I) understand is described here (p. 319):
One of the questions that naturally arises in the study of Anglicisms in Czech is whether the approximated forms reflect British (RP) or American (General American) pronunciation in the event that they differ for a given lexical item. The following six categories were considered:
b) alternation between [ɑː] and [æl: we found only one item of this kind in our sample: bypass [ˈbajpaːs], which is based on the British pronunciation form. In other recent words, pronunciation may vary: grant is pronounced uniformly as [ˈgrant], but Hugh Grant (despite his British origin) is often realized as [ˈgrɛnt]. The usual pronunciation of breakdance is [ˈbrɛjgdɛns];
On the whole, approximated forms are based on British pronunciation variants, with the notable exception of rhoticity, which is always maintained. Out of the six categories, it is only the [ɑː/æ] difference which is likely to introduce instability in the system of phonological approximation.
I think here the instability refers to the following: there are words in which the British English uses [ɑː] while the American English uses [æ], and there is no consistency as far as into which Czech vowel will this English vowel be turned once the word becomes a Czech Anglicism: sometimes the English vowel becomes [a], which is how Czech normally handles [ɑː], but other times the English vowel becomes [e], which is how Czech normally handles [æ]. The instability refers to this lack of pattern: sometimes it's one, sometimes the other, and there does not seem to be any rhyme or reason why it's one and not the other in any given case.
In the case of CGEL, I think the instability also refers to a lack of rhyme or reason, this time as far as when to use the nominative and when the accusative. The pattern of usage is pretty fixed in time (i.e. it is not diachronic), but it is not predictible on any general grounds whether in any particular instance native speakers prefer the nominative or the accusative. At best one can talk about tendencies.
Is that what CGEL means by instability in the system, or am I misunderstanding it?
Another question: is there a meaningful contrast between variation and instability, in their senses as they are used in the boldfaced sentence from CGEL?