People who natively speak a language that has grammatical cases do generally use them commonly and consistently.
Like all language features, case systems do also evolve, and it's quite common for there to be variation in case use between different dialects of a language, or e.g. between literary and colloquial language, but (at least from a descriptive viewpoint) this is not so much incorrect as simply different usage. In any case (pun not intended), there does not appear to be any clear tendency for case loss in colloquial or "uneducated" language; sometimes colloquial speech does lose case distinctions that are preserved in literary usage, but sometimes it also innovates new case patterns, or new uses for existing cases.
For example, as noted by Anixx, colloquial Russian sometimes applies case markers to words that are indeclinable according to traditional literary grammar. Similarly, from personal experience, I can attest that the case system in casual spoken Finnish is not significantly simpler or less expressive than in formal literary usage, despite the significant morphological and even grammatical differences between the two.1
The Vulgar Latin that you mentioned, and the Romance languages that evolved from it, are something of an interesting special case. While it's true that there's a strong tendency among these languages to simplify the noun gender and case system they inherited from Latin (while, at the same time, innovating several new grammatical features not found in classical Latin, such as definite articles), this process is best understood in the context of the significant linguistic mixing of spoken Latin with the indigenous (e.g. Celtic) languages of the local population during the expansion of the Roman empire, and later with the Germanic languages spoken by invaders during its decline. It's not so much that uneducated Latin-speakers just spontaneously started simplifying the language, but that the simplified Vulgar language evolved from the speech of people speaking Latin as a second language (and, often, learning it from people already speaking a vernacular version of it, with strong external influences), in a process not entirely unlike creolization.
In fact, as DavidC notes, inconsistent and/or radically simplified case usage tends to be characteristic not so much of uneducated speakers, but of non-native speakers whose first language has a weak (or significantly different) case system compared to the language they are trying to speak. This is because such speakers are unaccustomed to paying attention to case as a grammatical feature (or to the specific case structure of the language in question), and thus have trouble fitting it into their mental framework.
For instance, English uses prepositions and word order to mark many of the grammatical distinctions that several other languages mark using noun cases. As an instructive experiment, one might try to invert the situation, and consider the difficulties encountered by a native speaker of some language with a loose word order and few prepositions, when they attempt to learn English. For example, where a fluent English-speaker would say "Did you go to the theater?", such a person might come up with, for example, "Went you theater?" This is not a mistake any native speaker (past the age where they're capable of formulating coherent sentences at all, anyway) would make, but for a person just learning English as a second language, it could be quite plausible.
Similarly, where a fluent English-speaker would speak of going in a hurry by car to the show at the theater in the town by the lake, a non-native speaker unused to English prepositions might say they were going e.g. at a hurry in a car at the show in the theater at the town off the lake. Again, most native speakers would immediately see that something was wrong with that sentence, even though it's mostly understandable, but a non-native speaker unfamiliar with English grammar could easily have trouble picking the correct prepositions for phrases like that, just as an English-speaker unfamiliar with noun cases might have trouble picking the correct cases when speaking e.g. German or Russian or Finnish.
1) In fact, while colloquial Finnish has all but lost several grammatical features of the literary language, such as the possessive suffixes, the noun cases — of which Finnish has 15 or so — remain relatively unchanged (except for some morphological variation). The rare instrumental cases (abessive, comitative and instructive) do tend to get replaced by adpositions or other alternative constructions in casual speech, except in certain fixed expressions, but they're not very common in literary usage, either. On the other hand, modern spoken Finnish may be in the process of innovating a new comitative case ending: in casual speech (as well as in some traditional dialects), the postposition kanssa ("with") commonly contracts to kaa, and, especially when unstressed, often merges into the preceding noun as a clitic -kaa (e.g. colloq. tuu munkaa = "come with me"). When used so, it could be loosely analyzed as a novel case marker, even though it lacks several grammatical features of the "true" Finnish noun cases, such as case agreement between nouns and adjectives. Notably, the closely related Estonian language appears to have gone through essentially the same process several hundred years ago to acquire its current comitative case marker -ga.